Set Theory\ Equivalence Relations

Question

Let $U$ be a finite, non-empty set. Define a relation ∼ on $P(U)$ (the power set of U) as follows: for $A, B ∈ P(U), A ∼ B $if and only if $A ⊆ B.$ Is ∼ an equivalence relation? Prove your answer.

Not really sure how to go about this one. I assume you start with some arbitrary element of $A ⊆ B.$

Answer 1

Hint: One of the properties of an equivalence relation is that if $A\sim B$ then $B\sim A.$ What happen if you take $A=\emptyset ,B=U$?

Answer 2

for ~ to be an equivalence relation, it needs to satisfy 3 conditions.

1) reflexive: A~A (true)

2) symmetric: A~B <==> B~A. (not true)

3) transitive: A~B and B~C ==> A~C (true)