Let A = {–2, 2} and B = (0, 3, 5). Find:

(i) A × B

(ii) B × A

(iii) A × A

(iv) B × B

(i) Given: A = {-2, 2} and B = {0, 3, 5}

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, 2} and B = {0, 3, 5}. So,

A × B = {(-2, 0), (-2, 3), (-2, 5), (2, 0), (2, 3), (2, 5)}

(ii) Given: A = {-2, 2} and B = {0, 3, 5}

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, 2} and B = {0, 3, 5}. So,

B × A = {(0, -2), (0, 2), (3, -2), (3, 2), (5, -2), (5, 2)}

(iii) Given: A = {-2, 2}

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, 2} and A = {-2, 2}.So,

A × A = {(-2, -2), (-2, 2), (2, -2), (2, 2)}

(iv) Given: B = {0, 3, 5}

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 = {0, 3, 5} and B = {0, 3, 5}. So,

B × B = {(0, 0), (0, 3), (0, 5), (3, 0), (3, 3), (3, 5), (5, 0), (5, 3), (5, 5)}