Question

Let some elements of A*B (A cross B) are =(1,2),=(2,4) and n(A*B)=13. Is this possible? Why?

please answer, no pranks​

Answer 1

Answer:

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Step-by-step explanation:

Given, n(A)=4,n(B)=2

∴n(A×B)=8

Thus the number of subsets of A×B having at least 3 elements

=2

8

−

8

C

0

−

8

C

1

−

8

C

2

=256−1−8−28=219

Answer 2

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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