$F=ABCD'+AB'CD'+A'BC'D+AB'D'+A'B'CD+A'C'D+AB'CD$

Question

Need to solve by Boolean algebra. I tried but didn't solve it and the answer on K-map is $\;A'C'D+B'CD+ACD'+A'BC'$.

The question is $\;ABCD'+AB'CD'+A'BC'D+AB'D'+A'B'CD+A'C'D+AB'CD$.

Answer 1

HINT: Use the Adjacency principle: $PQ + PQ'=P$

For example: $ABCD'+AB'CD'=ACD'$

If for some reason you are not given Adjacency as a basic rule (and many textbooks don't which I never understand, since it's such a useful principle!), you can always derive it as follows from the rules that I am sure are given to you:

$PQ+PQ' \overset{\text{Distribution}}{=} P(Q + Q') \overset{\text{Complement}}{=} P\!\cdot\!1\overset{\text{Identity}}{=} P$

By the way, when you look at a K-map, you'll understand why this principle is called Adjacency: this is exactly the algebraic equivalent of the process of grouping together adjacent cells in a K-map