Question

Provide a counterexample to show that each statement is false.

Statement: If , then .

Short answer

For a counterexample, and , the statement is false.

Step-by-step solution

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

Step 2. State counterexample.

For the given statement “If $ab<0$, then $a<0$.” let the counterexample be $a=2$and $b=-1$.

Step 3. Verify the counterexample.

Here,

$\begin{array}{c}ab=2\times \left(-1\right)\\ =\left(-2\right)\end{array}$

So,$ab<0$$ab<0$

But, $a=2>0$, which contradict the statement $a<0$,

Thus, if $ab<0$, it does not necessary means $a<0$.

Therefore, for counterexample $a=2$and $b=-1$, the statement is false.