It is false that if p then q.

Question

I'm doing some homework in which I'm converting textual descriptions of logic statements to their respective symbolic representation.

If one reads It is false that if p then q.

I was wondering the typical representation of this.

i.e. Is it ~p -> q or ~(p -> q). Essentially what I'm asking is typically when converting a textual representation to a symbolic representation, do we assume that the negation applies to the entire expression, or simply the entity immediately following the negation.

Thanks.

Answer 1

Read it as

It is false that: "if $p$, then $q$".

So the (entire) statement $(p\implies q)$ should be logically negated.