Let A = {–1, 2, 3} and B = {1, 3}. Determine(i) A × B(ii) B × A(ii

1.	Let A = {–1, 2, 3} and B = {1, 3}. Determine(i) A × B(ii) B × A(iii) B × B(iv) A × A
Answer» According to the question, A = {–1, 2, 3} and B = {1, 3} (i) A × B {–1, 2, 3} × {1, 3} So, A × B = {(–1, 1), (–1, 3), (2, 1), (2, 3), (3, 1), (3, 3)} Hence, the Cartesian product = {(–1, 1), (–1, 3), (2, 1), (2, 3), (3, 1), (3, 3)} (ii) B × A. {1, 3} × {–1, 2, 3} So, B × A = {(1, –1), (1, 2), (1, 3), (3, –1), (3, 2), (3, 3)} Hence, the Cartesian product = {(1, –1), (1, 2), (1, 3), (3, –1), (3, 2), (3, 3)} (iii) B × B {1, 3} ×{1, 3} So, B × B = {(1, 1), (1, 3), (3, 1), (3, 3)} Hence, the Cartesian product = {(1, 1), (1, 3), (3, 1), (3, 3)} (iv) A × A {–1, 2, 3} × {–1, 2, 3} So, A × A = {(–1, –1), (–1, 2), (–1, 3), (2, –1), (2, 2), (2, 3), (3, –1), (3, 2), (3, 3)} Hence, the Cartesian product ={(–1, –1), (–1, 2), (–1, 3), (2, –1), (2, 2), (2, 3), (3, –1), (3, 2), (3, 3)}

Let A = {–1, 2, 3} and B = {1, 3}. Determine(i) A × B(ii) B × A(iii) B × B(iv) A × A

Answer»

According to the question,

A = {–1, 2, 3} and B = {1, 3}

(i) A × B

{–1, 2, 3} × {1, 3}

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

Hence, the Cartesian product = {(–1, 1), (–1, 3), (2, 1), (2, 3), (3, 1), (3, 3)}

(ii) B × A.

{1, 3} × {–1, 2, 3}

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

Hence, the Cartesian product = {(1, –1), (1, 2), (1, 3), (3, –1), (3, 2), (3, 3)}

(iii) B × B

{1, 3} ×{1, 3}

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

Hence, the Cartesian product = {(1, 1), (1, 3), (3, 1), (3, 3)}

(iv) A × A

{–1, 2, 3} × {–1, 2, 3}

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

Hence, the Cartesian product ={(–1, –1), (–1, 2), (–1, 3), (2, –1), (2, 2), (2, 3), (3, –1), (3, 2), (3, 3)}