(i) Given: A = {2, 3, 5} and B = {5, 7}

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 = {2, 3, 5} and B = {5, 7}. So,

A × B = (2, 3, 5) × (5, 7)

= {(2, 5), (3, 5), (5, 5), (2, 7), (3, 7), (5, 7)}

(ii) Given: A = {2, 3, 5} and B = {5, 7}

To find: B × A

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 = {2, 3, 5} and B = {5, 7}. So,

B × A = (5, 7) × (2, 3, 5)

= {(5, 2), (5, 3), (5, 5), (7, 2), (7, 3), (7, 5)}

(iii) Given: A = {2, 3, 5} and B = {2, 3, 5}

To find: A × A

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 = {2, 3, 5} and A = {2, 3, 5}. So,

A × A = (2, 3, 5) × (2, 3, 5)

= {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}

(iv) Given: B = {5, 7}

To find: B × 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, B = {5, 7} and B = {5, 7}. So,

B × B = (5, 7) × (5, 7)

= {(5, 5), (5, 7), (7, 5), (7, 7)}