Simplification with karnaugh maps

Question

I have 2 boolean equations, and I have to simplify them with karnaugh-maps, but I have a little problem understanding the procedure: First, I got this one: out = (~a * b * ~c * d) + (~a * b * c * d). This reduces to ~a * b * d. The bit changes at c, so c is irrelevant, no problem.

Now the problem: b * ~a + a * b * ~c this reduces to ~a * b+b * ~c. Here we have a bit change at c again, but ~c isn't irrelevant. Why?

Answer 1

Because there are two separate minterms, ~AB and B~C. Your first example only comprises of one minterm; your assumption about relevance only applies to individual minterms, not to the set of all minterms.