Question

If A and B are two sets having 3 elements in Common. If n(A)=5, n(B)= 4, then find the number

of elements in (A x B)∩(B x A).​

Answer 1

Answer:

Step-by-step explanation:

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.