To get right to the point. I have written a test which required me to Simplify to DNF. And the following equation gives me trouble. Here is the equation:
¬(¬x∨¬y∨¬z((x∨¬x)→0)→y
So from there I went like this:
=> (x∨¬x)→0)
=> (¬x∨x)→0) (commutative law)
=> (1→0)
=> (0)
=> ¬(¬x∨¬y∨¬z(1→0))→y
=> ¬(¬x∨¬y∨¬z(0)
=> ¬¬x∧¬¬y∧¬¬z(~0)→y (this was the one part the teach marked wrong.)
=> x∧y∧z(1)→y
=> x∧y∧z→y
=> (x∧y)→y
=> (¬(x∧y))∨y
=> (¬x∨~y)∨y
=> (¬x∨y)∨(¬y∨y)
=> (¬x∨y)∨(1) = 1
So I tried formatting it the best I could here. But I can not quite figure out as to why it is wrong.