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Write (a) the contrapositive and (b) the inverse of the following statement.

If those are red and white then this is blue.

Short Answer

Expert verified

a. The contrapositive of 鈥淚f those are red and white then this is blue鈥 is鈥淚f this is not blue then those are not red and white鈥.

b. The inverse of 鈥淚f those are red and white then this is blue鈥 is鈥淚f those are not red and white then this is not blue鈥.

Step by step solution

01

a.Step 1- Apply the concept of the contrapositive statement.

A contrapositive of any statement is the switching of hypothesis and the conclusion of the inverse of that statement such thatto form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

02

Step 2- Write the inverse of the statement.

Consider the statement 鈥淚f those are red and white then this is blue鈥.

Write the inverse of the conditional statement as follows:

If those are not red and white then this is not blue.

03

Step 3- Write the contrapositive of the statement.

Interchange the hypothesis and the conclusion of the inverse statement to write the contrapositive of the statement as follows:

If this is not blue then those are not red and white.

Therefore, the contrapositive of the statement is 鈥淚f this is not blue then those are not red and white鈥.

04

b.Step 1- Apply the concept of the inverse of a statement.

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

05

Step 2- Write the inverse of the statement.

Consider the statement鈥淚f those are red and white then this is blue鈥.

Take the negation of the hypothesis and the conclusion to write the inverse of the statement.

06

Step 3- Step description.

The negation of the hypothesis and the conclusion is 鈥淚f those are not red and white then this is not blue.鈥.

Therefore, the inverse of the statement is 鈥淚f those are not red and white then this is not blue鈥.

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