Question

Let A={1,2,3},B={a,b,} be two sets.

Write universal relation from A to B.

What is the number of non-empty relation from A to B

Answer 1

SOLUTION

GIVEN

A = {1,2,3} , B = {a,b} be two sets.

TO DETERMINE

1. Write universal relation from A to B.

2. The number of non-empty relation from A to B

EVALUATION

Here the given two sets are

A = {1,2,3} , B = {a,b}

Then

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

ANSWER TO QUESTION : 1

The universal relation from A to B

= A × B

= { (1,a), (1,b), (2,a) , (2,b), (3,a), (3,b) }

ANSWER TO QUESTION : 2

We see that

n(A×B) = 6

So the required number of non-empty relation from A to B

= The number of non empty subsets of A × B

$\sf{ = {2}^{6} - 1}$

$\sf{ = 64 - 1}$

$\sf{ = 63}$

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Answer 2

Step-by-step explanation:

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