This is about negations of if then statements and why they can't be if then statements.

Perhaps a Truth Table might shed some light on this. Below is a TT for "if p, then q."

p. q. if p, then q.

T. T. T.

T. F. F. [note this case. "if T, then F" = F.]

F. T. T.

F. F. T.

Notice that an implication "if p, then q" is only F when then premise, p, is T and the conclusion, q, is F.

This is also the only case the negation of an implication is T.

So considering this, we see that a negation of an "if-then", being true in only one case, cannot also be an "if-then", which is T in three cases.

Incidently, the negation of "if p, then q" is "p and (not q)."

Hope that helps.

## Comments

Yeah that helps a lot! Thanks so much!!

Your welcome!

Logic & Proof was one of my favorite courses.

Learning that "If [falsehood], then [anything]." was a logically true statement showed me how strangely entertaining math can be.

I also liked that the word "truer" has no place in logic. I like words, with a few exceptions. That one has always bothered me though. :)

Robert,this is just to let you know that your spelling of,"Your" should be,"You're welcome!" A lot of people get this wrong. Examples: Is that your car? and You're late! You're means you are.