(A) The set $X$ contains $50$ elements.$A = \{2, 4, 6, \dots, 50\}$,so $n(A) = \lfloor 50/2 \rfloor = 25$.$B = \{7, 14, 21, 28, 35, 42, 49\}$,so $n(B)

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(A) The set $X$ contains $50$ elements.$A = \{2, 4, 6, \dots, 50\}$,so $n(A) = \lfloor 50/2 \rfloor = 25$.$B = \{7, 14, 21, 28, 35, 42, 49\}$,so $n(B) = \lfloor 50/7 \rfloor = 7$.$A \cap B$ consists of multiples of $\text{lcm}(2, 7) = 14$,which are $\{14, 28, 42\}$. Thus,$n(A \cap B) = 3$.The smallest subset of $X$ containing both $A$ and $B$ is $A \cup B$.Using the formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$,$n(A \cup B) = 25 + 7 - 3 = 29$.

Class 11 Mathematics Set Theory Word Problem - Set Theory

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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

JEE MAIN 2020 All JEE MAIN

A
$29$
B
$26$
C
$31$
D
$34$

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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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