a Prove U is an equivalence relation e If the set is of all

a) Prove U is an equivalence relation

e) If the set is of all people, what type of relations are these? Explain why.

Solution

a.) As st is square,

So, it is reflexive and symeetric.

And as it is reflexive and symmetric, so, U is equivalence.

c.) For n elements, No of reflexive relations are

2^(n^2-n)

So, for 2 elements,

we have

2^(4-2)

So, 4 reflexive relations

d.) For symmetric relations,

n elements have 2^(n^2+n)/2 relations

So, for 2 elements,

2^3 = 8 symmetric relations.