Question

FIND: AxB,AxA,BxA. A={2,-2,3} and B={1,-4} ​

Answer 1

Concept

In mathematics, sets are the collection of well defined elements. Number of elements in the set is represented as the cardinal number of a set in {}. AxB set of all ordered pairs (a, b) where a ∈ A and b ∈ B. AxB = {(a,b) | a ∈ A and b ∈ B}. AxB does not equal BxA unless A=B or A or B is the empty set.

Given

A={2,-2,3} and B={1,-4}

Find

AxB, AxA, BxA.

Solution

A×B = {(2,1) (2,-4) (-2,1) (-2,-4) (3,1) (3,-4)}

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

B×A = {(1,2) (1,-2) (1,3) (-4,2) (-4,-2) (-4,3)}

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Answer 2

Answer:

A×B = {(2,1) (2,-4) (-2,1) (-2,-4) (3,1) (3,-4)}

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

B×A = {(1,2) (1,-2) (1,3) (-4,2) (-4,-2) (-4,3)}

Step-by-step explanation:

Sets are the collection of well defined elements.

Number of elements in the set is represented as the cardinal number of a set in {}.

AxB is theset of all ordered pairs (a, b) where a ∈ A and b ∈ B. AxB = {(a,b) | a ∈ A and b ∈ B}.

AxB does not equal BxA unless A=B or A or B is the empty set.

It is given that A={2,-2,3} and B={1,-4}

We need to determine AxB, AxA, BxA.

Hence,

A×B = {(2,1) (2,-4) (-2,1) (-2,-4) (3,1) (3,-4)}

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

B×A = {(1,2) (1,-2) (1,3) (-4,2) (-4,-2) (-4,3)}

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