Let the boolean function F=AB'C+A'BC+A'BC'+AB'C' is equivalent to

Question

Let the boolean function $F=AB'C+A'BC+A'BC'+AB'C'$ is equivalent to which of the following

1) B directsum C

2) A directsum B

3) C directsum A

4)A directsum B directsum C

Plz explain in details

Answer 1

You can pull out $C$ from the first two terms and $C'$ from the last two terms: $$F=(AB'+A'B)C\, +\, (A'B+AB')C'\ =\ (AB'+A'B) (C+C') $$ Here $C+C'=1$ and $AB'+A'B=A\oplus B=(A+B)(A'+B')$ is the symmetric difference (or direct sum).