Hello guys so I'm a bit skeptical about a problem:
Given: AB'+ AC + BC + D'C + DB'C'
how is the given equivalent to AB' + BC + D'C + DB'C'?
If so what rule to simply from AB'+ AC + BC + D'C + DB'C' to AB'+ BC + D'C + DB'C'?
I've tried most of the laws but i don't seem to get it. I've doubled check it with a truth table and they are equivalent. Would anyone help? I feel I'm not understating something silly. Any help would be appreciated. Thanks.
If both A and C are true, then as one of B and B' is true, one of AB' and BC must be true. Thus is the only case in the first expression which is not immediately obvious in the second one.
You could also draw up a truth table for AB' + AC + BC and see that it is, in fact, the same as the truth table for AB' + BC. Thinking in terms of K-maps, you could also see this as a group on the map which overlaps other groups and is redundant and can be removed.