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Chapter 2: Q2. (page 68)

Provide a counter example to disprove the statement:

If x2>4, then x>2.

Short Answer

Expert verified

The example that disproves the statement isx=鈭�3 as it satisfies the first statement but does not satisfy the second condition.

Step by step solution

01

Step 1. State the information.

If x2>4, then x>2.

02

Step 2. Provide the example.

The statement 鈥淚f x2>4, then x>2鈥� 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 鈥�3, it can be seen that, although it satisfies the first statement where 鈭�32>4, but it does not satisfy the conditionx>2 since 鈭�3<2 .

03

Step 3. State the conclusion.

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

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