Science:Math Exam Resources/Courses/MATH220/April 2005/Question 01/Hint 1

A theorem is always a statement of the type A $\Rightarrow$ B and since we have the equivalence

$\displaystyle A\Rightarrow B\equiv \lnot A\lor B$

we can deduce that the negation of such a statement is

$\displaystyle {\begin{aligned}\lnot (A\Rightarrow B)&\equiv \lnot (\lnot A\lor B)\\&\equiv A\land \lnot B\end{aligned}}$

Or in plain English: the negation of A implies B is when A is true and B isn't.