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 .