## I need to simplify these boolean expressions.

I need to simplify these boolean expressions.

1. The problem statement, all variables and given/known data

Problem A:
abd+abd+bcd+bcd+abcd+bcd

Problem B:
abcd+abd+abcd+abd+acd+abd+abcd

Problem C:
abcd+abcd+abd+abcd+bd+abd

2. Relevant equations

abc means a AND b AND c
a+b means a OR b
a` means NOT a

I have been working on these for over 6 hours and I still have a mess. I look at the rules and try to apply them, but I know my answers are incorrect.