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

• April 4th 2011, 07:34 AM
Pranas
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? :)
Using Boolean algebra logic I am asked to prove $\displaystyle $A \subseteq B \Rightarrow \overline B \subseteq \overline A$$
If $x\in A$ then $x\in B$ is equivalent to If $x\notin B$ then $x\notin A$.