Chapter 2: Q13 (page 35)

Provide a counterexample to show that each statement is false.
Statement: If point G is on $\vec{A B}$ ,then G is on $\vec{B A}$ .

Short Answer

Expert verified

The counterexample is the diagram, which 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 counterexample.

For the given statement “If point G is on $\vec{A B}$ , then G is on $\vec{B A}$ .” let the counterexample by the figure given below:

Step 3. Verify the counterexample.

Here, point G is on $\vec{A B}$ , because the line $\vec{A B}$ starts with A and then passes through point B and G, but the line $\vec{A B}$ is starts from B and passes through A and does not pass through G.

Thus, the line $\vec{B A}$ does not pass-through point G.

Therefore, the diagram is a counterexample that shows that the statement is false.

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Provide a counterexample to show that each statement is false.
Statement: If point G is on $\vec{A B}$ ,then G is on $\vec{B A}$ .

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State counterexample.

Step 3. Verify the counterexample.

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Provide a counterexample to show that each statement is false.Statement: If point G is on AB→,then G is onBA→.

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State counterexample.

Step 3. Verify the counterexample.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Provide a counterexample to show that each statement is false.
Statement: If point G is on $\vec{A B}$ ,then G is on $\vec{B A}$ .