Assume that B is a Boolean algebra with operations + and ·

.

For each true statement below, give a detailed proof. For each false statement below, write

out its negation, then give a proof of the negation.

(∀a, b ∈ B) (a + b = 1 ↔ b · ā = ā)

(∀a, b ∈ B) (a · b = 0 ↔ b + ā = ā)

(∀a, b ∈ B) (a + b = a + c → b = c)
for the last one, i had the same proof as

http://www.mathhelpforum.com/math-he...b-b-c-b-c.html
but it just doesn't seem right to me...

completely stumped on the first two

.

please help!!!!

thanks!!!