Answer : (i) Given: A = {-3, -1} and B = {1, 3} To find: A × B
By the definition of the Cartesian product,
Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.
P × Q = {(p, q) : p Є P, q Є Q}
Here, A = {-3, -1} and B = {1, 3}. So,
A × B = {-3, -1} × {1, 3}
= {(-3, 1), (-3, 3), (-1, 1), (-1, 3)}
(ii) Given: C = {3, 5}
From part (i), we get A × B = {(-3, 1), (-3, 3), (-1, 1), (-1, 3)}
So,
(A × B) × C = {(-3, 1), (-3, 3), (-1, 1), (-1, 3)} × (3, 5)
= (-3, 1, 3), (-3, 1 , 5), (-3, 3, 3), (-3, 3, 5), (-1, 1, 3), (-1, 1, 5), (-1, 3, 3), (-1, 3, 5)}