Question

If Number of Elements in Set A is 'p' and Number of Elements in Set B is 'q' then Prove that ,

(1) The Number of Possible relations from A to B is \sf{{2}^{pq}}2pq

(2) The Number of Possible Reflexive Relations on A = \sf{{2}^{p(p-1)}}2p(p−1)

Irrelevant answers will be reported .



​

Answer 1

Answer:

Given A and B are two sets with number of elements p and q respectively.

The cartesian product of A and B=A×B={(a,b):(a∈A) and (b∈B)}

Number of elements in A×B=∣A×B∣=∣A∣.∣B∣=pq

Any relation from A to B is a subset of A×B.

Hence number of relations from A to B is the number of subsets of A×B

=2

∣A×B∣

=2

pq

Explanation:

Please mark me as Brainliest and Also Thank my answer