Question

If A= 1, 3, 5 , and B = 2, 3, then findA x B and B x A.

Answer 1

A × B = {(1,2),(1,3),(3,2),(3,3),(5,2),(5,3)}

B × A = {(2,1),(2,3),(2,5),(3,1),(3,3),(3,5)}

Answer 2

SOLUTION

GIVEN

A = {1, 3, 5} and B = {2, 3}

TO DETERMINE

A × B and B × A

CONCEPT TO BE IMPLEMENTED

CARTESIAN PRODUCT :

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

EVALUATION

Here the given sets are

A = {1, 3, 5} and B = {2, 3}

Now we have

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

∴ A × B = { (1,2) , (1,3) , (3,2) , (3,3) , (5,2) , (5,3) }

Again we have

$\sf{B \times A = \{(x, y) : x \in B \: \: and \: \: y \in A \}}$

∴ B × A = { (2,1) , (2,3) , (2,5) , (3,1) , (3,3) , (3,5) }

FINAL ANSWER

A × B = { (1,2) , (1,3) ,(3,2) ,(3,3) , (5,2) , (5,3) }

B × A = { (2,1) , (2,3) , (2,5) , (3,1) , (3,3) , (3,5) }

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