For practicing I grabbed two logical functions that both represent a XOR Gate. I want to show that these functions are equivalent:
$$ a\overline{b}+\overline{a}b \iff (a+b)(\overline{a}+\overline{b}). $$
Both functions are taken from Wikipedia.
For now I've come this far:
$$ \begin{align*} (a+b) (\overline{a}+\overline{b}) &= (a+b) \overline{(ab)} \\ & = \overline{(\overline{a}\overline{b})} \space \overline{(ab)} \\ & = (\overline{a}\overline{b}) + (ab). \end{align*} $$ I have no idea how to go on. I would appreciate if you could state the rules you used in your solution.
It's much simpler.
$$ (a+b)(\overline{a}+\overline{b}) = a \overline{a} + b \overline{b} + a \overline{b} + b \overline{a} $$
Now the first two terms on the RHS are zero since an expression (like $a$) cannot be simultaneously true and false. That's it.