Simplify the following equations using the theorems and axioms of Boolean algebra. Your goal in each case (a) to (c) is to simplify as much as possible. You must show all simplifying steps clearly along with the theorem or axiom you used (just write the abbreviated theorem or axiom name like T1, A1 etc.) Note: we will use the prime notation to write the inverse/complement of a variable i.e. write the apostrophe after the variable name. E.g. A' is the complement of A.

Y = AC + A'B'C

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

Y = A'B'C'D' + AB'C' + AB'CD' + ABD + A'B'CD' + BC'D + A'

Y = A'BC + A'BC'