Step-by-step explanation:
Let the elements in both sets are:
A = {p,q,r,s,t}
B = {p,q,r,u}
We have, n(A) = 5, n(B) = 4
(i) n(A * B)
= n(A) * n(B)
= 5 * 4
= 20
(ii) n[(A * B) ∩ (B * A)]
(A * B) = (p,p),(p,q),(p,r),(p,u),(q,p),(q,q),(q,r),(q,u),(r,p),(r,q),(r,r),(r,u),(s,p),(s,q),(s,r),(s,u),(t,p),(t,q),(t,r),(t,u)
(B * A) = (p,p),(p,q),(p,r),(p,s),(p,t),(q,p),(q,q),(q,r),(q,s),(q,t),(r,p)(r,q),(r,r),(r,u),(r,t),(u,p),(u,q),(u,r),(u,s),(u,t)
∴ (A * B) ∩ (B * A) = {(p,p),(p,q),(p,r),(q,p),(q,q),(q,r),(r,p),(r,r),(r,u)}
Therefore, n[(A * B) ∩ (B * A)] = 9
Hope it help you!
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Answers & Comments
Step-by-step explanation:
Let the elements in both sets are:
A = {p,q,r,s,t}
B = {p,q,r,u}
We have, n(A) = 5, n(B) = 4
(i) n(A * B)
= n(A) * n(B)
= 5 * 4
= 20
(ii) n[(A * B) ∩ (B * A)]
(A * B) = (p,p),(p,q),(p,r),(p,u),(q,p),(q,q),(q,r),(q,u),(r,p),(r,q),(r,r),(r,u),(s,p),(s,q),(s,r),(s,u),(t,p),(t,q),(t,r),(t,u)
(B * A) = (p,p),(p,q),(p,r),(p,s),(p,t),(q,p),(q,q),(q,r),(q,s),(q,t),(r,p)(r,q),(r,r),(r,u),(r,t),(u,p),(u,q),(u,r),(u,s),(u,t)
∴ (A * B) ∩ (B * A) = {(p,p),(p,q),(p,r),(q,p),(q,q),(q,r),(r,p),(r,r),(r,u)}
Therefore, n[(A * B) ∩ (B * A)] = 9
Hope it help you!