Let A = {–1, 2, 3} and B = {1, 3}. Determine

(i) A × B (ii) B × A

(iii) B × B (iv) A × A

Given: A = {–1, 2, 3} and B = {1, 3}

To find: (i) A × B (ii) B × A (iii) B × B (iv) A × A

Explanation:

(i) A × B

The sets A = {–1, 2, 3} and B = {1, 3} are given; we need to find the Cartesian product of set A and set B.

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

So, this is the required Cartesian product.

(ii) The sets B = {1, 3} and A = {–1, 2, 3} are given; we need to find the Cartesian product of set B and set A.

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

So this is the required Cartesian product.

(iii) The sets B = {1, 3} and B = {1, 3} are given; we need to find the Cartesian product of set A and set B.

So, B×B = {(1, 1), (1, 3), (3, 1), (3, 3)}

So this is the required Cartesian product.

(iv) The sets A = {–1, 2, 3} and A = {–1, 2, 3} are given; we need to find the Cartesian product of set A and set B.

So, A×A = {(-1, -1), (-1, 2), (-1, 3), (2, -1), (2, 2), (2, 3), (3, -1), (3, 2), (3, 3)}

So this is the required Cartesian product.