In Boolean algebra, simplification of expressions using algebraic laws helps…

(a)
Using identity: (X + Y)(X + Z) = X + YZ
Let X = AB
F = AB + CD

(b)
F = Y(X + X̄Y)
= Y·X + Y·X̄Y
= XY + YX̄Y
= XY + X̄Y
= Y(X + X̄)
= Y·1
= Y

(c)
F = AB + BC + B'C
= AB + C(B + B')
= AB + C·1
= AB + C

(d)
F = A + A'B
= (A + A')(A + B)
= 1·(A + B)
= A + B

(e)
F = A'B'C + A'BC + AB'
= A'C(B' + B) + AB'
= A'C·1 + AB'
= A'C + AB'

Thus, all expressions are simplified using Boolean algebra laws.