How to negate an implication in English? How to negate this proposition:
"If $xy$ is irrational then either $x$ is irrational or $y$ is irrational. "
Because the negation of $p\Rightarrow q$ is $p \wedge \text{not } q$. If I translate this sentence into English, it would be "$xy$ is irrational and $x$ and $y$ are rational." It is so strange. 

This is a bit of a weird question, because the statement you are trying to negate is true!
But you are right. The negation of this statement is: 
There exists x and y which are rational such that xy is irrational.
