Question

2. Let some elements of A x B are (1,3),(2,4) and
n(Ax B)=13. Is this possible ?why?​

Answer 1

SOLUTION :-

GIVEN :-

Let some elements of A×B are (1,3),(2,4) and n(A×B)=13

TO CHECK

IS this possible?Why?

CONCEPT TO BE IMPLEMENTED

Let A & B are two non empty sets then their cartesian product is denoted by A × B and defined as

A × B = { (a, b) : a ∈ A & b ∈ B }

EVALUATION

Here it is given that some elements of A × B are (1,3),(2,4)

So two of all elements of A are 1 , 2

Similarly two of all elements of B are 3 , 4

So the minimum number of elements of both sets A & B are 2

Again it is given that n(A×B)=13

∴ n(A) × n(B) = 13

Since 13 is prime

So either n(A) = 1 & n(B) = 13 or n(A) = 13 & n(B) = 1

Which contradicts that the minimum number of elements of both sets A & B are 2

Hence the given statement is impossible

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Answer 2

Solution ⤵️

Given ⤵️

Let some elements of A×B are (1,3),(2,4) and n(A×B)=13

To Find ⤵️

Is this possible?Why?

Concept to be used here ⤵️

Let A & B are two non empty sets then their cartesian product is denoted by A × B and defined as:-

A × B = { (a, b) : a ∈ A & b ∈ B }

Calculation ⤵️

Here it is given that some elements of A × B are (1,3),(2,4)

So two of all elements of A are 1 , 2

Similarly two of all elements of B are 3 , 4

So the minimum number of elements of both sets A & B are 2

Again it is given that n(A×B)=13

∴ n(A) × n(B) = 13

Since 13 is prime

Therefore, either n(A) = 1 & n(B) = 13 or n(A) = 13 & n(B) = 1

Which contradicts that the minimum number of elements of both sets A & B are 2.

Therefore the given statement is impossible.

━━━━━━━━━━━━━━━━

Hope it helps !!

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