Question

(i) If A = {1, 2, 3} and B = {2, 4}, state the elements of AxA, AxB, BxA, BxB, (AxB)∩(BxA)
(ii) If A = {-1, 1}, find AxAxA.

Answer 1

concept: if A ={a,b} and B= {c, d }

then, A × B = {(a,c), (a, d), (b, c), (b, d)}

(i) A = {1, 2, 3} and B = {2, 4}

then, A × A = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

A × B = {(1, 2), (1,4), (2,2), (2,4), (3, 2), (3, 4)}

B × A = {(2, 1), (2,2), (2,3), (4,1), (4,2), (4,3)}

B × B = {(2,2), (2,4), (4,2), (4,4)}

(A × B) $\cap$(B × A) = (2,2)

(ii) A = {-1, 1}

then, A × A = {-1, 1} × {-1, 1}

A × A = {(-1, -1), (-1, 1), (1, -1), (1, 1)}
Now, 
By definition A × A × A = {(a,b,c) : a,b,c Є A}.

⇒ A × A × A = {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (1, -1, -1), (-1, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}