Question

Provide a counter example to disprove the statement:

If $x^2>4$, then $x>2$.

Short answer

The example that disproves the statement is$x=-3$ as it satisfies the first statement but does not satisfy the second condition.

Step-by-step solution

Step 1. State the information.

If $x^2>4$, then $x>2$.

Step 2. Provide the example.

The statement “If $x^2>4$, then $x>2$” is not necessarily true for all values of x. This can be proved by considering negative values of x. For example, considering the value of x as –3, it can be seen that, although it satisfies the first statement where ${\left(-3\right)}^2>4$, but it does not satisfy the condition$x>2$ since $-3<2$ .

Step 3. State the conclusion.

Therefore, for the statement can be disproved by usingnegative values of x.