Answer:
Algebraic Theorem Proofs
Step-by-step explanation:
We have to prove the following in the question:
Theorems used:
[tex]XX' = 0\\X + 1 = X\\X + 0 = X\\X+X'=1\\XX = X\\X+X=X[/tex]
(a) X(X′ + Y) = XY
[tex]X(X'+ Y) \\=XX'+XY\\=0+XY\\=XY[/tex]
(b) X + XY = X
[tex]X + XY \\=X(1+Y)\\=XY[/tex]
(c) XY + XY′ = X
[tex]XY + XY'\\=X(Y+Y')\\=X(1)\\=X[/tex]
(d) (A + B)(A + B′) = A
[tex](A + B)(A + B')\\=AA + AB' +BA + BB'\\=A + A(B+B')+0\\=A+A(1)\\=A[/tex]
