Let X = {n in N : 1 leq n leq 50}. If A = {n | vedclass

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(A) The set $X$ contains integers from $1$ to $50$,so $n(X) = 50$.Set $A$ contains multiples of $2$ up to $50$: $A = \{2, 4, 6, \dots, 50\}$. The numb

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$29$

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(A) The set $X$ contains integers from $1$ to $50$,so $n(X) = 50$.Set $A$ contains multiples of $2$ up to $50$: $A = \{2, 4, 6, \dots, 50\}$. The number of elements is $n(A) = \lfloor 50/2 floor = 25$.Set $B$ contains multiples of $7$ up to $50$: $B = \{7, 14, 21, 28, 35, 42, 49\}$. The number of elements is $n(B) = \lfloor 50/7 floor = 7$.The intersection $A \cap B$ contains multiples of $	ext{lcm}(2, 7) = 14$ up to $50$: $A \cap B = \{14, 28, 42\}$. The number of elements is $n(A \cap B) = 3$.The smallest subset of $X$ containing both $A$ and $B$ is the union $A \cup B$.Using the inclusion-exclusion principle,$n(A \cup B) = n(A) + n(B) - n(A \cap B) = 25 + 7 - 3 = 29$.

Let $X = \{n \in N : 1 \leq n \leq 50\}$. If $A = \{n \in X : n \text{ is a multiple of } 2\}$ and $B = \{n \in X : n \text{ is a multiple of } 7\}$,then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

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