First slide

Operations on Sets

Question

$Statement 1 : If B = U - A then n (B) = n (U) - n (A) where U is universal set.$
$Statement 2 : For any three arbitrary sets A, B, C we have if C = A - B then n (C) = n (A) - n (B) .$

Moderate

A

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
B

statement I is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
C

Statement 1 is true, statement 2 is false
D

statement 1 is false, statement 2 is true.

Solution

$If U is universal set then B = U - A = A^{'}, for which n (B) = n (A^{'}) = n (U) - n (A)$
$But for any three arbitrary sets A, B, C we cannot have always n (C) = n (A) - n (B) if C = A - B as it is not specified here that$
$weather A is universal set or not. In case A is not universal set we cannot conclude that n (C) = n (A) - n (B) .$
Hence, statement 1 is true but statement 2 is false.

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