Q4A. Give the counterexample of the g... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 1: Q4A. (page 56)

Give the counterexample of the given conditional statement.
If $a b > 0$ then $a$ and $b$ are greater than 0.

Short Answer

Expert verified

A counterexample to the given conditional statement is when $a = 鈭� 3$ and $b = 鈭� 2$ . The hypothesis is true; $(鈭� 3) 脳 (鈭� 2) = 6 > 0$ . However, the conclusion, $鈭� 3 > 0$ and $鈭� 2 > 0$ is false.

Step by step solution

Step 1. State the concept.

The product of two positive numbers and of two negative numbers are both positive.

Step 2. List the given data.

The given statement is 鈥淚f $a b > 0$ , then, $a$ and $b$ are greater than 0.鈥� Here, the hypothesis is 鈥� $a b > 0$ 鈥� and the conclusion is 鈥� $a$ and $b$ are greater than 0鈥�.

Step 3. Simplify the given statement.

The given statement implies that if the product of two numbers is positive, then both these numbers are also positive. However, it is known that the product of two negative numbers is also positive.

Step 4. Give a counterexample.

Consider $a = 鈭� 3$ and $b = 鈭� 2$ .

Then,

$\begin{array}{l} a b = (鈭� 3) (鈭� 2) \\ = 6 \end{array}$

So, $a b > 0$ . Thus, the hypothesis is true.

However, $a = 鈭� 3 < 0$ and $b = 鈭� 2 < 0$ . This implies that the conclusion, 鈥� $a$ and $b$ are greater than 0鈥� is false.

So, $a = 鈭� 3$ and $b = 鈭� 2$ is a counterexample of the given conditional statement.

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91影视

Give the counterexample of the given conditional statement.
If $a b > 0$ then $a$ and $b$ are greater than 0.

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. List the given data.

Step 3. Simplify the given statement.

Step 4. Give a counterexample.

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91影视

Give the counterexample of the given conditional statement.If ab>0then aand bare greater than 0.

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. List the given data.

Step 3. Simplify the given statement.

Step 4. Give a counterexample.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Give the counterexample of the given conditional statement.
If $a b > 0$ then $a$ and $b$ are greater than 0.