Is this the simplified version of this boolean expression? Or is this reviewer wrong

Question

Cause I've tried doing the truth table unfortunately one has 3 literals and the other has 4 so i got confused.

F = (A+B+C)(A+B+D')+B'C;

and this is the simplified version

F = A + B + C

http://www.belley.org/etc141/Boolean%20Sinplification%20Exercises/Boolean%20Simplification%20Exercise%20Questions.pdf

cause I think there's something wrong with this reviewer.. or is it accurate? btw is simplification different from minimizing from Sum of Minterms to Sum of Products?

Answer 1

Yes, it is the same.

Draw the truth table for both expressions, assuming that there are four input variables in both. The value of D will not play into the second truth table: values in cells with D=1 will match values in cells with D=0. In other words, you can think of the second expression as

F = A +B + C + (0)(D)

You will see that both tables match: the (A+B+C)(A+B+D') subexpression has zeros in ABCD= {0000, 0001, 0011}; (A+B+C) has zeros only at {0000, 0001}. Adding B'C patches zero at 0011 in the first subexpressions, so the results are equivalent.