Question

to verify that for two sets A and B, n(A×B) = pq and the total number of relations from A to B is 2^pq , where n(A) = p and n(B) = q .​

Answer 1

Answer:

Taking left hand side ,we get_

n(A×B)

by using distributive identity (a(b+c) =A×B +A×C)

n×A +n×B

by putting values of n(a) and n(b) in the equation ,we get_

p×q

=pq

Here, pq =pq

LHS = RHS

Hence, verified.

Step-by-step explanation:

Answer 2

Given,

n(A) = p

n(B) = q

To prove,

n(A x B) = p*q

The total number of relations from A to B is 2^(p*q)

Solution,

The following proof may be used to support the above claims.

Considering the Left-Hand Side of the equation to prove,

⇒ n (A x B)

By Distributive Identity,

( ∴ a(b + c) = ab + ac )

⇒ n(A) x n(B)

Now,

It is given that n(A) = p and n(B) = q.

⇒ p x q

(L.H.S = R.H.S)

(Hence Proved)

Furthermore,

The relations from A to B are accounted to be 2^(p x q).

As a result, both propositions are proven and expressed in this manner.