Question

Let A = {1, 2, 3, 4, 5}, B = {2, 3, 6, 7}, then number of elements in
(A × B) ∪ (B × A) is ?

Answer 1

Answer :

Given that,

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

So, (A × B)

= { (a, b) : a ∈ A, b ∈ B }

= { (1, 2), (1, 3), (1, 6), (1, 7), (2, 2), (2, 3), (2, 6), (2, 7), (3, 2), (3, 3), (3, 6), (3, 7), (4, 2), (4, 3), (4, 6), (4, 7), (5, 2), (5, 3), (5, 6), (5, 7) }

and (B × A)

= { (b, a) : b ∈ B, a ∈ A }

= { (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5) }

Now, (A × B) U (B × A)

= { (1, 2), (1, 3), (1, 6), (1, 7), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (4, 2), (4, 3), (4, 6), (4, 7), (5, 2), (5, 3), (5, 6), (5, 7), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5) }

∴ n {(A × B) U (B × A)} = 36

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