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Chapter 6: Q7. (page 210)

Classify the following conditional as true or false. Then state its inverse and contrapositive and classify each of these as true or false.

If a triangle is not isosceles, then it is not equilateral.

Short Answer

Expert verified

The statement is true.

Contrapositive: If a triangle is equilateral, then it is an isosceles- True.

Inverse: If a triangle is an isosceles, then it is an equilateral- False

Step by step solution

01

Step 1. Apply the concept of conditional statement and contrapositive.

Conditional statements are thosestatements where a hypothesis is followed by a conclusion. It is also known as an " If-then" statement.

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

02

Step 2. Apply the concept of the inverse of a conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

03

Step 3. Step description.

Consider the conditional statement 鈥淚f a triangle is not isosceles, then it is not equilateral鈥� and it is a true statement.

Write the contrapositive, inverse, and converse of the conditional statement as follows:

Inverse: If a triangle is an isosceles, then it is an equilateral- False statement.

Contra positive: If a triangle is equilateral, then it is an isosceles- True statement.

Therefore, the conditional statement is true and its contrapositive is true and inverse is false.

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