When using the Consensus Theorem in Boolean algebra to minimize an expression, is it a legal move to find and add a redundant term to the expression and then use that term to find more redundant terms and then eliminate all of them?
For instance:
F = A'B + AC + B'A
If XY = AC and X'Z = A'B, then YZ = BC, so:
F = A'B + AC + B'A + BC
Then if XY = BC and X'Z = B'A, then YZ = AC
AC and BC are (possibly?) redundant terms, so drop them both:
F = A'B + B'A
Is this legal, or is it an odd hack/mathematical abomination?
There's something off, since the Venn diagrams don't match. You can legally do your first step. At that point, you may replace BC+B'A by BC+B'A+AC using consensus. There are now five terms, A'B+AC+BC+B'A+AC. Of course the two copies of AC may be combined, so at this point you just have four terms A'B+B'A+AC+BC. This time the Venns do match with the original A'B+AC+BA. [You now have four terms instead of the starting three, so perhaps not much was gained.] However there can't be a way to express the set in question without mentioning C somehow, as the Venn shows that C goes along a border of the final region and cuts it.
Note: In this example in a way the final +BC in A'B+AB'+AC+BC is redundant, since dropping it happens not to affect the resulting set. But I don't (immediately) see an "automatic" way to drop it using a simple rule. [I'm no expert on this consensus topic though.]