Question

Let A={p, q, r, s}, B = {p, q, r} and C ={ q, s}. Find all sets X such that a) X is a subset of B and also a subset of C. B) X is a subset of A but not a subset of B
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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

Step-by-step explanation:

I guess this is the answer