4.

If A = {a, b, c} and B = {p, q}, then find :

(i) A x B (ii) B x A (iii) A x A (iv) B x B (v) n (A x B) (vi) n (B x A) (vii) n (A x A) (viil) n (B x B).

(i) A  X B = {a, b, c} x (p, q} = {{a, p}, {a, q}, (b, p}, {b, q}, {c, p}, {c, q}}

(ii) B x A = {p, q} x {a, b, c} = {{p, a, }.{p, b}.{p, c}.{q, a}.{q, b}.{q, c}}

(iii} A x A = {a, b, c} x {a, b, c} = {(a, a), (a, b), (a, c), (b,l, a), (b,, b), (b, c), (c a), (c, b), (c, c)}

(iv) B x B = {p.q} x {p.q} = {(p.p), (p.q), (p.q), (p.q)

(v) n(A x B) = n(A) x n(B) = 3 x 2 = 6

(vi) n(B xA) = n(B) x n(A) = 2 x 3 = 6

(vii) n(A xA) = n(A)  x n(A) = 3 x 3 = 9

(viii) n(B x B) = n(B) x n(B) = 2 x 2 = 4