Zeal Patel Let a and b be elements in a Boolean algebra. Prove that: ( a . boc ) + boc = boc ( a + b + c ) o ( b + c ) = b + c a) Let x and y be elements of a Boolean Algebra such that x + y = 0 . Prove that x = y = 0 b ) Let x and y be elements of a Boolean Algebra such that x o y = 1 . Prove that X = y = 1 Let x, y, z be elements of a Boolean algebra. Prove that x+ yo (x + z) = (x+ y) o (x+z) For the following claim determine whether it is always true or whether it may be false in some cases . In a Boolean Algebra , It is never the case that x = x . Justify your answer . Let x, y E B where B is a Boolean Algebra. 107 Prove x + y = x o y if and only if x = y