# Thread: Proofs involving sets and their compliments

1. ## Proofs involving sets and their compliments

Prove that A is a subset of B iff B' is subset of A'

2. Originally Posted by instrument.santosh
Prove that A is a subset of B iff B' is subset of A'
i would prove both direction via a direct proof

so to start you off

(=>) Assume $A \subseteq B$. Then, $x \in A \implies x \in B$. Now, let $y \in B'$ .....(you want to show that this implies $y \in A'$)

(<=) For the converse, assume $B' \subseteq A'$. Then $x \in B' \implies x \in A'$. Now, let $y \in A$.....(you want to show that this implies $y \in B$)

now continue