Truth table for logic equation

Question

1. Given the following logic equation, draw the equivalent truth table:

         _       _  _     _         _ _      

Z = ABC + ABC + ABC + ABC + ABC

please show steps

Answer 1

Z = AB'C + A'B'C + A'BC + A'B'C + ABC

= AB'C + A'C (B' + B) + A'B'C + ABC

= AC(B' + B) + A'C.1 + A'B'C

= C (A + A') + A'B'C

= C (1 + A'B')

= C