Let X = \ n ∈ N: 1 ≤ n ≤ 50\ . If A = \ n ∈ X: nisamultipleof2\ and B = \ n ∈ X: nisamultipleof7\ , then the number of elements in the smallest subset of X , containing both A and B , is.

Correct answer: 29 Here, A = \ 2, 4, 6, . . . . 50\ and B = \ 7, 14, . . . 49\ Required smallest subset is A B . So, n(A B) = n(A) + n(B) - n(A B) = 25 + 7 - 3 = 29 .

JEE Main 20207 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2020 · 7 January · Evening Shift · Mathematics · Sets and Relations

Let X = \ n ∈ N: 1 ≤ n ≤ 50\ . If A = \ n ∈ X: nisamultipleof2\ and...

Let

X = \left\{n \in N: 1 \le n \le 50\right\}

. If

A = \left\{n \in X: nisamultipleof2\right\}

and

B = \left\{n \in X: nisamultipleof7\right\}

, then the number of elements in the smallest subset of

X

, containing both

A

and

B

, is.

Correct answer

Step-by-step solution

Here, $A = \left\{2, 4, 6, . . . . 50\right\}$ and $B = \left\{7, 14, . . . 49\right\}$

Required smallest subset is $A \cup B$ .

So, $n\left(A \cup B\right) = n\left(A\right) + n\left(B\right) - n\left(A \cap B\right)$
$= 25 + 7 - 3$
$= 29$ .

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