If A and B are two sets having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A x B) and n[(A x B) ∩ (B x A)].

Question

Philoid · Accepted Answer

given: (A) = 5 and n(B) = 4

To find: [(A × B) ∩ (B×A)]

n (A × B) = n(A) × n(B) = 5 x 4 = 20

n (A ∩ B) = 3 (given: A and B has 3 elements in common)

In order to calculate n [(A × B) ∩ (B × A)], we will assume

A = (x, x, x, y, z) and B = (x, x, x, p)

So, we have

(A × B) = {(x, x), (x, x), (x, x), (x, p), (x, x), (x, x), (x, x), (x, p), (x, x), (x, x), (x, x), (x, p), (y, x), (y, x), (y, x), (y, p), (z, x), (z, x), (z, x), (z, p)}

(B × A) = {(x, x), (x, x), (x, x), (x, y), (x, z), (x, x), (x, x), (x, x), (x, y), (x, z), (x, x), (x, x), (x, x), (x, y), (x, z), (p, x), (p, x), (p, x), (p, y), (p, z)}

[(A × B) ∩ (B × A)] = {(x, x), (x, x), (x, x), (x, x), (x, x), (x, x), (x, x), (x, x), (x, x)}

∴ We can say that n [(A × B) ∩ (B × A)] = 9