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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.

Sipko
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  • It is extremely confusing what you're even trying to do there. How are all those lines related, and what do the => at the beginning of each of them mean? – hmakholm left over Monica May 31 '15 at 23:16
  • Also, your first line has three ( but only two ) in it; are some symbols missing from it? In particular, the symbols z( cannot follwo each other in a well-formed formula. – hmakholm left over Monica May 31 '15 at 23:19
  • the => symbols are just there to mark the next step. @Henning Makholm Thats a typo and the formula was given to me that way from the teacher. – Sipko May 31 '15 at 23:42

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