Simplify the following functions using Boolean algebra:

Question

Y_1=ABC + AB'C'+AB'C.

Y_2=A'BC' + AB'C + AB'C'.

Answer 1

For Y_1:

ABC + AB'C' + AB'C

= AB(C + C') + AB'C

= AB + AB'C

= AB(1 + C)

= AB

For Y_2:

A'BC' + AB'C + AB'C'

= AB'C' + AB'C + A'BC'

= AB'C'(1 + C) + A'BC'

= AB'C' + A'BC'

= BC'(A' + A)

= BC'