Simplify this Boolean Expression
A & ~((~A) & (~B)).
According to the truth table I did it should be equivalent to ~B but I can't get the boolean algebra to work out to that.
A & ~((~A) & (~B))
= A & (~~A or ~~B) Demorgan's law
= A & (A or B) Double negation
= (A & A) or (A & B) Distributive Property
And this is where I get stuck. If A&A = just A then you get into an infinate loop of distrubutive properties and never reach your goal.