Question

Ay Let A = {1,2,3,4,5} , B={2,3,6,7} . Then the no.
of clements in (AXB) n (BXA) is
​

Answer 1

Answer:

We have to find out (A × B) ∩ (B × A).

Given that A = {1, 2, 3, 4, 5} and B = {2, 3, 6, 7}

We have to use the identities given below:

1. A ∩ B = B ∩ A

2. (A × B) ∩ (C × D) = (A ∩ C) × (B ∩ D)

According to the 2nd identity,

(A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A)

According to the 1st identity,

(A ∩ B) × (B ∩ A) = (A ∩ B) × (A ∩ B)

Thus,

(A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B)

Now we have to find A ∩ B.

A ∩ B = {2, 3}

So,

(A ∩ B) × (A ∩ B)

⇒ {2, 3} × {2, 3}

⇒ {(2, 2), (2, 3), (3, 2), (3, 3)}

Hence. (A × B) ∩ (B × A) has 4 elements.

|(A × B) ∩ (B × A)| = 4

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