Conditional Statements

Question

Regarding conditional reasoning, I know p->q means that p is sufficient for happening q. I was wondering how "not sufficient statement" can be shown in this terminology?

Answer 1

While there is not a single symbol, you can use the laws of logic to rewrite it in a couple of ways: $$\neg(p \implies q) \quad \iff \quad \neg(\neg p \, OR \, q) \quad \iff \quad p \,\, AND \,\, \neg q $$ In words, "$p \implies q$" is false if and only if $p$ is true and $q$ is false.

Answer 2

There is no real sign for this but you may use ¬(p→q)

Answer 3

The negator operator $\neg$ (or sometimes !) is what you are looking for. For example: q doesn't imply p: $$\neg(q \Rightarrow p)$$