Chapter 2: Q14 (page 35)

Provide a counterexample to show that each statement is false.
Statement: If $x y > 5 y$ , than $x > 5$ .

Short Answer

Expert verified

The counterexample, $x = 3$ and $y = - 6$ , shows that 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 the counterexample

In order to show, “If $x y > 5 y$ , then $x > 5$ .” is false let $x = 3$ and $y = - 6$ .

Step 3. Verify the counterexample.

If $x = 3$ and $y = - 6$ , then

$\begin{matrix} x y = (3) (- 6) \\ = (- 18) \end{matrix}$

and,

$\begin{matrix} 5 y = 5 \times (- 6) \\ = (- 30) \end{matrix}$

Since, $(- 18) > (- 30)$ , hence $x y > 5 y$ . But, $x = 3 < 5$ , thus, $x < 5$ ,which contradicts the inequality.

Therefore, the counterexample, $x = 3$ and $y = - 6$ , shows that the statement is false.

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Provide a counterexample to show that each statement is false.
Statement: If $x y > 5 y$ , than $x > 5$ .

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State the counterexample

Step 3. Verify the counterexample.

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Provide a counterexample to show that each statement is false.Statement: If xy>5y, than x>5.

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State the counterexample

Step 3. Verify the counterexample.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Probability and Statistics

Pure Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Provide a counterexample to show that each statement is false.
Statement: If $x y > 5 y$ , than $x > 5$ .