Question

Prove the following properties of Boolean algebras. Give a reason for each step. 1.(x.y)+(x′.z)+(x′.y.z′)=y+(x′.z) 2.x.y+x′=y+x′.y′ 3.x.y+y.z.x′=y.z+y.x.z′...

Prove the following properties of Boolean algebras. Give a reason for each step.

1.(x.y)+(x′.z)+(x′.y.z′)=y+(x′.z)

2.x.y+x′=y+x′.y′

3.x.y+y.z.x′=y.z+y.x.z′

Prove that for any Boolean algebra:

a. If x+y=0,then x=0 and y=0.

b. x = y if and only if x . y′ + y .x′ = 0.

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