Write the following Boolean expression in product of sums form?

Question

Write the following Boolean expression in product of sums form:

a'b + a'c' + abc

is it correct if I write it as the following ?

(a+b')(a+c)(a'+b'+c')

Answer 1

The original expression

(!a and b) or (!a and !c) or (a and b and c)

is equivalent to

(b and c) or (!a and !c)

             ab
       00  01  11  10
      +---+---+---+---+
   0  | 1 | 1 | 0 | 0 |
c     +---+---+---+---+
   1  | 0 | 1 | 1 | 0 |
      +---+---+---+---+

Written as product of disjunctions

(!a or c) and (b or !c)