First slide

Operations on Sets

Question

Let $X = \{n \in N : 1 \leq n \leq 50\}$ . If $A = \{n \in X : n i s a m u l t i p l e o f 2\}$ and $B = \{n \in X : n is a multiple of 7\}$ . Then the number of elements in the smallest subset of X containing both A and B is _____

Easy

Solution

We have A $A = \{2, 4, 6, 8 . . . . . . . . 50\}, B = \{7, 14, 21, 28, 35, 42, 49\} a n d A \cap B = \{14, 28, 42\}$
Also the smallest subset containing both A and B is $A \cup B$
$∴ n (A \cup B) = n (A) + n (B) - n (A \cap B)$ = 25 + 7 – 3 = 29

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