If aN = { ax : x ∈ N } then the set 4 N ∩ 6 N is
The shaded region in the given figure is
In statistical survey of 1003 families of Kolkata, it was found that 63 families has neither a radio nor a TV 794 families has a radio and I87 has TV. The number of families in that group having both a radio and a TV is
If A , B and C are non-empty sets, then ( A − B ) ∪ ( B − A ) =
The shaded region in the given figure is
Which of the following is not the solution of | x + 3 | + x x + 2 >1?
Which of the following is a null set?
If a N = { a x : x ∈ N } , then the set 3 N ∩ 7 N is
Two finite sets have m and n(m, n) elements. The number of subsets of the first set is 112 more than that of the second set. The value of mn is
The number of integral values of x is 5 x − 1 < ( x + 1 ) 2 < 7 x − 3 , is
If A and B are two given sets, then A ∩ ( A ∩ B ) c is equal to
Let U be the universal set and A ∪ B ∪ C = U . Then [ ( A − B ) ∪ ( B − C ) ∪ ( C − A ) ] C equals
If A = { 2 , 3 , 5 } , B = { 2 , 5 , 6 } , then ( A − B ) × ( A ∩ B ) is
If x satisfies | x − 1 | + | x − 2 | + | x − 3 | ≥ 6 , then
A relation from P to Q is
Let A = a , b , c and B = 1 , 2 . Consider a relation R defined from set A to set B. Then R is equal to set
The relation R defined on the set A = { 1 , 2 , 3 , 4 , 5 } by R = x , y : x 2 – y 2 < 16 is given by
If R = x , y | x , y ∈ z , x 2 + y 2 ≤ 4 is a relation in Z, then domain of R is
If A = [ x , y : x 2 + y 2 = 25 ] and B = x , y : x 2 + 9 y 2 = 144 , then A ∩ B contains
Set A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A ∪ B
The set A = { x : | 2 x + 3 | < 7 } is equal to
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, each having at least three element is
When A=∅, then number of elements in P(A) is
If X ∪ { 1 , 2 } = { 1 , 2 , 3 , 5 , 9 } , then which of the following is not true?
Given n ( U ) = 20 , n ( A ) = 12 , n ( B ) = 9 , n ( A ∩ B ) = 4 , where U is the universal set, A and B are subsets of U , then n ( A ∪ B ) C =
The largest interval for which x 12 − x 9 + x 4 − x + 1 > 0 is
A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then a value of x can be
Let A and B be two sets, then ( A ∪ B ) C ∪ A C ∩ B equals
In a certain town, 25% families own a phone and families 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard: 1. 10% families own both a car and a phone. 2. 35% families own either a car or a phone. 3. 40,000 families live in the town. Which of the above statements are correct?
Consider following statements (i) P ( A ) ∪ P ( B ) = P ( A ∪ B ) (ii) P ( A ) ∩ P ( B ) = P ( A ∩ B ) , then
Solution set of the inequality 1 2 x − 1 > 1 1 − 2 x − 1 is
The set of all real numbers x for which x 2 − | x + 2 | + x > 0 is
If n ( A − B ) = 14 , n ( A ∪ B ) = 29 and n ( A ∩ B ) = 9 , then n ( B − A ) is
In a class of 60 students, 25 students play cricket and 20 play tennis. If 10 students play both the games, then the number of students who play neither game is .
Let A and B be two sets, then ( A ∪ B ) C ∪ A C ∩ B equals
If A and B are events such that P ( A ¯ ∪ B ¯ ) = 3 4 , P ( A ¯ ∩ B ¯ ) = 1 4 and P ( A ) = 1 3 , then P ( A ¯ ∩ B ) is
Suppose A 1 , A 2 , … , A 30 are thirty sets each having 5 elements and B 1 , B 2 , … , B n are n sets each with 3 elements. Let ∪ i = 1 30 A i = ∪ i = 1 n B j = S and each element of S belongs to exactly 10 of the A i ‘s and exactly 9 of the B j ‘s. Then n is equal to
If A = { x : x is a multiple of 4 } and B = { x : x is a multiple of 6 } , then A ∩ B consists of all multiples of ?
If ‘ R ′ be a relation defined as a R b iff | a − b | > 0 , then the relation is ( a , b ∈ R )
Given log 10 2 = a and log 10 3 = b . If 3 x + 2 = 45 , then the value of 1 − a b =
Let U be the universal set and . Then [ ( A − B ) ∪ ( B − C ) ∪ ( C − A ) ] ′ equals
A survey shows that 63% of the people watch a news channel whereas, 76% watch an entertainment channel at a particular time. lf x% of the people watch both types of channels, then
If set A = x ∣ x 2 ( 5 − x ) ( 1 − 2 x ) ( 5 x + 1 ) ( x + 2 ) < 0 and set B = x ∣ 3 x + 1 6 x 3 + x 2 − x > 0 , then A ∩ B does not contain
Number of integers satisfying the inequality, x 4 − 29 x 2 + 100 ≤ 0 is
Let n ( A ) = n . Then the number of all relations on A is
The number of reflexive relations of a set with four elements is equal to
If X = 8 n – 7 n – 1 ; n ∈ N and Y = { 49 ( n – 1 ) ; n ∈ N } , then
If N a = an : n ∈ N , then N 3 ∩ N 4 =
Let A = {1 {2, 3}}. Then, the number of subsets of A, is
If X = 4 n − 3 n − 1 : n ∈ N and Y = { 9 ( n − 1 ) : n ∈ N } where N is the set of natural numbers, then X ∪ Y is equal to
The set A = x : x ∈ R , x 2 = 16 and 2 x = 6 is equal to
If aN = { an : n ∈ N } and bN ∩ cN = dN where a , b , c ∈ N and, b,c are coprime, then
Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m n is .
Let A, B and C be sets such that ϕ ≠ A ∩ B ⊆ C .Then which of the following statements is not true?
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are
If A = { 2 , 3 } , B = { 4 , 5 } and C = { 5 , 6 } , then n { ( A × B ) ∪ ( B × C ) } is
If two sets A and B are having 99 elements in common the number of elements common to each of the sets AxB and Bx A are 121 λ 2 the value of λ is
Let A = {1,2,3} and B= {2,3,4}, then which of the following relations is a function from A to B
If the sets A and B are defined as A = ( x , y ) : y = e x , x ∈ R ; B = { ( x , y ) : y = x , x ∈ R } , then
Suppose A 1 , A 2 , A 3 , … … . , A 30 are thirty sets each having 5 elements and B 1 , B 2 , … … , B n , are n sets each with 3 elements. Let ∪ i = 1 30 A i = ∪ j = 1 n B j = S and each elements of S belongs to exactly 10 of the A i ′ s and exactly 9 of the B j ′ s . Then n is equal to
If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4, 6, 8, 10, 12, 14, 16, 18} and N, the set of natural numbers is the universal set, then A ‘ ∪ [ ( A ∪ B ) ∩ B ‘ ] is
If A, B, C are three sets such that A ∩ B = A ∩ C a n d A ∪ B = A ∪ C , then
If X and Y are two sets such that X ∩ Y = X ∪ Y , then
If A and B are two sets such that n ( A ∪ B ) = 36 , n ( A ∩ B ) = 16 and n ( A ~ B ) = 15 , then n ( B ) is equal to
If A and B both contain same number of elements and are finite sets then
A , B , C are three sets such that n ( A ) = 25 , n ( B ) = 20 , n ( c ) = 27 , n ( A ∩ B ) = 5 , n ( B ∩ C ) = 7 and A ∩ C = ∅ then n ( A ∪ B ∪ C ) is equal to
If A Δ B = A ∪ B then
If the relation R : A B , where A = { 1 , 2 , 3 } and B = { 1 , 3 , 5 } is defined by R = { ( x , y ) : x < y , x ∈ A , y ∈ B } , then
If A , B , C are three non-empty sets such that A ∩ B = ϕ , B ∩ C = ϕ , then
The relation R defined on the set A = { 1 , 2 , 3 , 4 , 5 } by R = ( x , y ) : x 2 − y 2 < 16 is given by
Let A = {1, 2, 3} and B = {3, 8} Statement-1: ( A ∪ B ) × ( A ∩ B ) = { ( 1 , 3 ) , ( 2 , 3 ) , ( 3 , 3 ) ( 8 , 3 ) } Statement-2: ( A × B ) ∩ ( B × A ) = { ( 3 , 3 ) }
Among employee of a company taking vacations last years, 90 % took vacations in the summer , 65 % in the winter, 10 % in the spring, 7 % in the autumn, 55 % in winter and summer, 8 % in the spring and summer, 6 % in the autumn and summer, 4 % in the winter and spring , 4 % in winter and autumn, 3 % in the spring and autumn, 3 % in the summer, winter and spring, 3 % in the summer, winter and autumn, 2 % in the summer, autumn and spring, and 2 % in the winter, spring and autumn. Percentage of employee that took vacations during every season:
From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. The largest possible number that could have passed all three exams is
Let X and Y be two sets. Statement 1: X ∩ ( Y ∪ X ) ′ = ϕ Statement 2: If X ∪ Y has m elements and X ∩ Y has n elements then symmetric difference X ∆ Y has m – n elements.
The relation R defined on the set A = 1 , 2 , 3 , 4 , 5 by R = ( x , y ) : | x 2 – y 2 | < 16 is given by
If a set A has n elements then the number of all relations on A is
Suppose A 1 , A 2 , ….., A 30 are thirty sets each having 5 elements and B 1 , B 2 ……… , B n are n sets each with 3 elements, let ∪ i = 1 30 A i = ∪ j = 1 n B j = S and each element of S belongs to exactly 10 of the A i ’s and exactly 9 of the B j ’s. Then n is equal to
Let I be the set of integers, N the set of non-negative integers; Np the set of non-positive integers ; E is the set of even integers and P is set of prime numbers. Then
If n ( A ) = n then n { ( x , y , z ) ; x , y , z ∈ A x ≠ y , y ≠ z , z ≠ x } =
Of the number of three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team, 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is
If A = 3 n : n ∈ N , n ≤ 6 , B = 9 n : n ∈ N , n ≤ 4 then which of the following is false
Let X = n ∈ N : 1 ≤ n ≤ 50 . If A = n ∈ X : n i s a m u l t i p l e o f 2 and B = n ∈ X : n is a multiple of 7 . Then the number of elements in the smallest subset of X containing both A and B is
Let U be the universal set and A ∪ B ∪ C = U . Then ( A − B ) ∪ ( B − C ) ∪ ( C − A ) C equals
If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A × B and B × A is
If A = { ϕ , { ϕ } } , then the power set of A is
If A and B are two sets then ( A − B ) ∪ ( B − A ) ∪ ( A ∩ B ) =
If X = 8 n − 7 n − 1 , n ∈ N and y = { 49 n − 49 , n ∈ N } t h e n
If A and B are two given sets, then A ∩ ( A ∩ B ) C is equal to
Consider the following relations: 1. A − B = A − ( A ∩ B ) 2. A = ( A ∩ B ) ∪ ( A − B ) 3. A − ( B ∪ C ) = ( A − B ) ∪ ( A − C ) Which of these is/are correct?
If set A and B are defined as: A = ( x , y ) : y = 1 x , x ≠ 0 , x ∈ R B = { ( x , y ) : y = − x , x ∈ R } , then
Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then
Which is the simplified representation of A ′ ∩ B ′ ∩ C ∪ ( B ∩ C ) ∪ ( A ∩ C ) where A , B , C are subsets of set X ?
If n ( A ) = 4 , n ( B ) = 3 , n ( A × B × C ) = 24 , then n ( C ) =
The number of elements in the set ( a , b ) : 2 a 2 + 3 b 2 = 35 , a , b ∈ Z } , where Z is the set of all integers, is
In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is
At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 arc doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors are attending the conference?
If A = [ − 3 , 7 ] and B = [ 2 , 9 ] then which of the following is not true
Solution of 1 x − 2 < 4 is
Solution of x + 1 x > 2 is
Number of integral values of x satisfying the inequation x x + 2 ≤ 1 | x | is
Number of real solution(s) of the equation | x − 3 | 3 x 2 − 10 x + 3 = 1 is
A survey shows that 63% of the people watch a news channel whereas 76% watch another TV channel. If x% of the people watch both the channels, then
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively,
Let A = x ∣ x 2 − 4 x + 3 < 0 , x ∈ R ; B = x ∣ 2 1 − x + p ≤ 0 ; x 2 − 2 ( p + 7 ) x + 5 ≤ 0 If B ⊆ A , then p ∈
The value of log 9 4 1 2 3 6 − 1 2 3 6 − 1 2 3 6 − 1 2 3 ⋯ ∞ is
Set of all values of x satisfying the equation | x + 1 | = 5 − | x − 4 | is
The number of integers satisfying log 1 x 2 ( x − 2 ) ( x + 1 ) ( x − 5 ) ≥ 1 is
When A = ϕ , then number of elements in P ( A ) is ….. here P(A) is set of all subsets of A
If sets A and B are disjoint sets, such that n ( A ∪ B ) = 30 and n ( A ) = 14 , then n ( B ) =
In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is
A survey shows that 63 % of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, then least value of x is
Suppose A 1 , A 2 , … , A 30 are thirty sets each having 5 elements and B 1 , B 2 , … , B n are n sets each with 3 elements. Let ∪ i = 1 30 A i = ∪ i = 1 n B j = S and each element of S belongs to exactly 10 of the A i ‘s and exactly 9 of the B j ‘s. Then n is equal to
In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is
Statement 1 : If B = U − A then n ( B ) = n ( U ) − n ( A ) where U is universal set. Statement 2 : For any three arbitrary sets A , B , C we have if C = A − B then n ( C ) = n ( A ) − n ( B ) .
If ( x − 3 a ) ( x − a − 3 ) < 0 ∀ x ∈ [ 1 , 3 ] then exhaustive set of values of a is
Let N be the set of non-negative integers, I the set of integers, N p the set of non-positive integers, E the set of even integers and P the set of prime numbers. Then
If n ( A ) = 3 , n ( B ) = 6 and A ⊆ B . Then the number of elements in A ∪ B is equal to
Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set. The respective values of m and n are
Solution of 0 < 3 x + 1 < 1 3 is
Suppose A 1 , A 2 , … , A 30 are thirty sets each having 5 elements and B 1 , B 2 , … , B n are n sets each with 3 elements. Let ∪ i = 1 30 A j = ∪ j = 1 n B j = S and each element of S belongs to exactly 10 of the A i ‘s and exactly 9 of the B j ‘s. Then n is =
Which of the following Venn diagrams is not correct for the set given?
If S = { x ∣ x is a positive multiple of 3 and less than 100 } and P = { x ∣ x is a prime number less than 20 } . Then n ( S ) + n P
Let F 1 be the set of parallelograms, F 2 the set of rectangles, F 3 be the set of rhombuses, F 4 be the set of squares and F 5 be the set of trapeziums in a plane. Then F 1 may be equal to
If n(A) = 3, n(B) = 6 and A ⊆ B . Then the number of elements in A ∪ B is equal to
If the sets A and B are defined as A = { ( x , y ) ∣ y = 1 / x , x ≠ 0 , x ∈ R } B = { ( x , y ) ∣ y = − x , x ∈ R , } Then
Let A and B be two non-empty subsets of a set X such that A is not a subset of B. Then
The set A ∩ B ′ ′ ∪ ( B ∩ C ) is equal to
For sets A and B, ( A ∪ B ) ′ ∪ A ′ ∩ B equals
Which is the simplified representation of A ′ ∩ B ′ ∩ C ∪ ( B ∩ C ) ∪ ( A ∩ C ) where A, B and C are subsets of set X?
In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% buy newspaper B and 10% buy newspaper C. Also,5o families buy newspapers A and B, 3% buy newspapers B and C and 4% buy newspapers A and C. lf 2% families buy all the three newspapers, then number of families which buy newspaper A only is
complete solution set of inequality ( x + 2 ) ( x + 3 ) ( x − 2 ) ( x − 3 ) ≤ 1 is
A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then
If A and B any two sets, then ( A ∩ B ) ‘ is equal to
20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is
If A and B are two sets, then A × B = B × A if
Let A and B be subsets of a set X. Then
Let A and B be two sets in the universal set. Then A – B equals
If A, B and C are any three sets, then A – ( B ∩ C ) is equal to
If A, B, C are three sets, then A ∩ B ∪ C is equal to
If A = 1 , 2 , 4 , B = 2 , 4 , 5 , C = 2 , 5 , then A – B × B – C is
If 1 , 3 , 2 , 5 and 3 , 3 are three elements of A × B and the total number of elements in A × B is 6, then the remaining elements of A × B are
A = 1 , 2 , 3 and B = 3 , 8 , then A ∪ B × A ∩ B is
If A = 2 , 3 , 5 , B = 2 , 5 , 6 , then A – B × A ∩ B is
In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is
If n ( A ) = 4 , n ( B ) = 3 , n ( A × B × C ) = 24 , then n ( C ) =
The number of elements in the set a , b : 2 a 2 + 3 b 2 = 35 , a , b ∈ Z , where Z is the set of all integers, is
If A = 1 , 2 , 3 , 4 , 5 , B = 2 , 4 , 6 , C = 3 , 4 , 6 , then A ∪ B ∩ C is
If A = 1 , 2 , 3 , 4 ; B = a , b and f is a mapping such that f : A B , then A × B is
If A = x , y then the power set of A is
A set contains 2 n + 1 elements. The number of subsets of this set containing more than n elements is equal to
Consider the following relations: 1 A – B = A – A ∩ B 2 A = A ∩ B ∪ A – B ( 3 ) A – ( B ∪ C ) = A – B ∪ A – C Which of these is/are correct
A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100, Physics 70, Chemistry 40; Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone
If A = { x : x is a multiple of 4 } and B = { x : x is a multiple of 6 } then A ⊂ B consists of all multiples of
If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A × B and B × A are
Given n U = 20 , n A = 12 , n B = 9 , n A ∩ B = 4 , where U is the universal set, A and B are subsets of U, then n ( A ∪ B C ) =
Let A = 1 , 2 , 3 . The total number of distinct relations that can be defined over A is
Let X = 1 , 2 , 3 , 4 , 5 and Y = 1 , 3 , 5 , 7 , 9 . Which of the followingis not relations from X to Y
Given two finite sets A and B such that n ( A ) = 2 , n ( B ) = 3 . Then total number of relations from A to B is
The relation R is defined on the set of natural numbers as a , b : a = 2 b . The R – 1 is given by
The relation R defined on the set of natural numbers as a , b : a differs from b by 3 , is given by
If R is a relation from a set A to set B and S is a relation from B to a set C, then the relation SoR
If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
A relation R is defined from 2 , 3 , 4 , 5 to 3 , 6 , 7 , 10 by xRy ⇔ x is relatively prime to y. Then domain of R is
R is a relation from 11 , 12 , 13 to 8 , 10 , 12 defined by y = x – 3 . Then R – 1 is
Let R be a relation of N defined by x + 2 y = 8 . The domain of R is
Solution set of x ≡ 3 ( mod 7 ) , p ∈ Z , is given by
Let R = 1 , 3 , 2 , 2 , 3 , 2 and S = 2 , 1 , 3 , 2 , 2 , 3 be two relations on set A = 1 , 2 , 3 . Then RoS =
If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is
If A = [ x : x is a multiple of 3 ] and B = [ x : x is a multiple of 5 ] , A – B is ( A means complement of A )
If A = x : x 2 – 5 x + 6 = 0 , B = 2 , 4 , C = 4 , 5 , then A × ( B ∩ C )
In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The no. of newspaper is
If A = { ϕ , { ϕ } } then the power set of A is
If A and B are two sets, then A = B ∩ C and B = C ∩ A then
Suppose . A 1 , A 2 , … , A 30 are thirty sets each having 5 elements and B 1 , B 2 , … , B n are n sets each having 3 elements. let ∪ i = 1 30 A i = ∪ j = 1 n B j = S and each elements of S belongs to exactly 10 of A i ‘ s and exactly 9 of B i ‘ s The value of n is equal to
Let A, B and C be finite sets such that A ∩ B ∩ C = ϕ and each one of the sets AΔB , BΔC and CΔA has 100 elements. The number of elements in A ∪ B ∪ C is
Let A ={1, 2,3, 4}, B = {2, 4, 6}. Then, the number of sets C such that A ∩ B ⊆ C ⊆ A ∪ B is
Let A = R x R, R the real number system and R = { ( ( x , y ) , ( a , b ) ) ∈ A × A ∣ either x< a or x = a and y > b} Then, which one of the following is true, if (x, y) ( a , b ) ) ∈ R and ( ( a , b ) ∈ R and ( ( a , b ) , ( p , q ) ) ∈ R ?
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is
If P, Q and R are subsets of a set A, then R × P c ∪ Q c c
If aN = { ax : x ∈ N } and bN ∩ cN = dN , where b , c ∈ N are relatively prime, then
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are
Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then
If A = [ x : f ( x ) = 0 ] and B = [ x : g ( x ) = 0 ] then A ∩ B will be
If A = { 1 , 2 , 3 , 4 , 5 } , then the number of proper subsets of A is
If n ( A ) = 3 and n ( B ) = 6 and A ⊆ B Then the number of elements in A ∩ B is equal to
If A = {1, 2, 3} , B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x is greater than y’. The range of R is
Let I be set of integers, N = the set of non-negative integers, N p = the set of non-positive integers. Then the sets A and B satisfying A ∩ B = ∅ are
Which of the following equality is not true.
A boating club consists of 82 members, each member is either a sailboat owner or a powerboat owner. If 53 members owned sailboats and 38 members owned powerboats, the number of members owned both sailboat and powerboat is
If, B ⊂ ≠ A ‘ , then which of the following sets is equal to A ‘ ,.
Let P = P = { θ : s i n θ – c o s θ = 2 c o s θ } a n d { Q = θ : s i n θ + c o s θ = 2 s i n θ } be two sets, then
Let U be a Universal set and n ( U ) = 12 . If A , B ⊆ U are such that n ( B ) = 6 and n ( A ∩ B ) = 2 then n ( A ∪ B ‘ ) is equal to
If x 2 + x 3 = 5 x 6 , then x is any term of the following
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X , Z ⊆ X and Y ∩ Z is empty is
If A = { 2 , 3 , 4 , 5 , 7 } , B = { 1 , 2 , 4 , 7 , 9 } then ( ( A ~ B ) ∪ ( B ~ A ) ) ∩ A is equal to
If A = { 2 x : x ∈ N } , B = { 3 x : x ∈ N } and C = { 5 x : x ∈ N ) then A ∩ ( B ∩ C ) is equal to
If X , Y and A are three sets such that A ∩ X = A ∩ Y and A ∪ X = A ∪ Y then
If A = { x : x ∈ R and satisfy x 2 − 15 x + 56 = 0 B = { x : x ∈ N and x + 5 ≤ 14 } and C = { x : x ∈ N and x / 112 } . Then A ∪ ( B ∩ C ) is equal to
If A is the set of letters needed to spell “ MATH-EMATICS” and B is the set of letters needed to spell STATISTICS, then
Let X = x : x = n 3 + 2 n + 1 , n ∈ N and Y = x : x = 3 n 2 + 7 , n ∈ N then
A , B , C are the sets of letters needed to spell the words STUDENT, PROGRESS and CONGRUENT, respectively. Then n ( A ∪ ( B ∩ C ) ) is equal to
Let A = { x : x is a prime factor of 240 } B = { x : x is the sum of any two prime factors of 240 } . Then
In a class 60 % passed their Physics examination and 58 % passed in Mathematics. Atleast what percentage of students passed both their Physics and Mathematics examination?
If A ∆ B = A ∪ B then
If A = { 1 , 2 , 3 , 4 } , B = { 3 , 4 , 5 } then the number of elements in ( A ∪ B ) × ( A ∩ B ) × ( A Δ B ) is
For non-empty subsets A and B ,
if A = { x : x ∈ I , − 2 ≤ x ≤ 2 } , B = { x ∈ I , 0 ≤ x ≤ 3 } , C = { x : x ∈ N , 1 ≤ x ≤ 2 } and D = { x , y ) ∈ N × N ; x + y = 8 } Then.
If n ∣ q and A = z ∈ C : z n = 1 B = z : z q = 1 then
If A = { z : ( 1 + 2 i ) z ¯ + ( 1 − 2 i ) z + 2 = 0 } and B = { z : ( 3 + 2 i ) z ¯ + ( 3 − 2 i ) z + 3 = 0 } then
E , I , R , O denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true
If the number of elements in ( A ~ B ) ~ C , ( B ~ C ) ~ A , ( C ~ A ) ~ B and A ∩ B ∩ C is 10 , 15 , 20 and 5 respectively then the number of elements in ( A ∆ B ) ∆ C is
Let A = ( x , y ) : x > 0 , y > 0 , x 2 + y 2 = 1 and let B = ( x , y ) : x > 0 , y > 0 , x 6 + y 6 = 1 Then A ∩ B
