NDA 2016 Maths · Mathematics · Sets, Relations and Functions · easy

Let A=\1,2,3,4\ and B=\2,4,6\. The number of elements in (A× B)∩(B× A) is

Single correct option

Let

A=\{1,2,3,4\}

and

B=\{2,4,6\}

. The number of elements in

(A\times B)\cap(B\times A)

Show answer and solution

Answer: (B) $4$

An ordered pair lies in both products only if its first entry is in

A\cap B

and its second entry is in

B\cap A

. Hence

(A\times B)\cap(B\times A)=(A\cap B)\times(A\cap B)

with

A\cap B=\{2,4\}

, giving

2\times2=4

pairs. The value 12 is

n(A\times B)

alone, and 2 counts only the common elements.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake