Chapter 6.2, Problem 1WE

(a)

To determine

To Write: the contrapositive of the statement “ $\text{If}n=17,\text{then 4}n=68$ ”.

Answer to Problem 1WE

  $\text{If}4n\ne 68,\text{then }n\ne 17$

Explanation of Solution

Given:

  $\text{If}n=17,\text{then 4}n=68$

Calculation:

A contrapositive of any statement is the switching of hypothesis and the conclusion of any statement.

Contrapositive is.

  $\text{If}4n\ne 68,\text{then }n\ne 17$

(b)

To determine

To Write: the inverse of the statement “ $\text{If}n=17,\text{then 4}n=68$ ”.

Answer to Problem 1WE

  $\text{If}n\ne 17,\text{then }4n\ne 68$

Explanation of Solution

Given:

  $\text{If}n=17,\text{then 4}n=68$

Calculation:

Inverse of the statement is when both hypothesis and conclusion are negated.

Inverse is.

  $\text{If}n\ne 17,\text{then }4n\ne 68$