Proof by contradiction using counterexample Why can't we use one counterexample as the contradiction to the contradicting statement?
Example:
Let a statement be A where a-->b.
We can prove A is not true by finding a counter example.
Now, in another space and time, Let a new statement be B where it is the same as a-->not b.
Why can't we prove B is not true by finding a counter example?
Thus, a contradiction and A is true?

Remember that:
$(a\implies b) \equiv (\neg a \lor b)$
Hence: $\therefore \neg (a\implies b) \equiv (a \land \neg b)$
The counter example of the implication is an event where $a$ happens and not $b$.
${\begin{array}{|c|c|c|c|}\hline a & b & a\to b & a \land \neg b \\ \hline\hline F & F & T & F \\\hline F & T & T & F \\ \hline T & F & F & \color{red}{T} \\\hline T & T & T & F \\ \hline  \end{array}}$
