Question

Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the

number of elements in (A × B)  (B × A) is

a) 18 b) 6 c) 4 d) 0​

Answer 1

$\huge{\underline{\underline{\mathbb{\pink{ANSWER}}}}}$

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

Answer 2

Step-by-step explanation:

Let's find (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)

Therefore,

(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

Here's your answer

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