# Thread: Proof of the subset equality (using Boolean algebra logic)

1. ## Proof of the subset equality (using Boolean algebra logic)

Using Boolean algebra logic I am asked to prove

$\displaystyle $A \subseteq B \Rightarrow \overline B \subseteq \overline A$$

In mathematical analysis course that looks like plain and simple modus tollens principle, but using Boolean algebra logic I just don't know...

Maybe you can help me?

2. Originally Posted by Pranas
Using Boolean algebra logic I am asked to prove $\displaystyle $A \subseteq B \Rightarrow \overline B \subseteq \overline A$$
In mathematical analysis course that looks like plain and simple modus tollens principle, but using Boolean algebra logic I just don't know...
That is just the contra-positive of a statement.
"If P then Q" is true then "If not Q then not P" is also true.
If $x\in A$ then $x\in B$ is equivalent to If $x\notin B$ then $x\notin A$.