(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)}

(iii) Given: B = {1, 3} and C = {3, 5}

To find: B × C

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, B = {1, 3} and C = {3, 5}. So,

B × C = (1, 3) × (3, 5)

= {(1, 3), (1, 5), (3, 3), (3, 5)}

(iv) Given: A = {-3, -1}

From part (iii), we get B × C = {(1, 3), (1, 5), (3, 3), (3, 5)}

So,

A × (B × C) = {-3, -1} × {(1, 3), (1, 5), (3, 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)}