Chapter 6.2, Problem 9WE

To determine

To Complete: The table by writing contrapositive, converse and inverse of the statement “ $\text{If }-2n<6,\text{ then }n>-3$ ”.

Answer to Problem 9WE

	Statements	$\text{If }-2n<6,\text{ then }n>-3$	True, $\begin{array}{l}-2n<6\\ -n<3\\ n>-3\end{array}$
1	Contrapositive	$\text{If }n<-3,\text{ then}-2n>6$	True, $\text{If }n<-3,\text{ then}-2n>6$
2	Converse	$\text{If }n>-3,\text{ then}-2n<6$	True, $\begin{array}{l}n>-3\\ 2\times n>2\times \left(-3\right)\\ 2n>-6\\ -2n<6\end{array}$
3	Inverse	$\text{If }-2n>6,\text{ then }n<-3$	True, $\begin{array}{l}-2n>6\\ -n>3\\ n<-3\end{array}$

Explanation of Solution

Given:

Statement is.

  $\text{If }-2n<6,\text{ then }n>-3$

Table is given as.

  

Calculation:

Table is completed as shown below.

	Statements	$\text{If }-2n<6,\text{ then }n>-3$	True, $\begin{array}{l}-2n<6\\ -n<3\\ n>-3\end{array}$
1	Contrapositive	$\text{If }n<-3,\text{ then}-2n>6$	True, $\text{If }n<-3,\text{ then}-2n>6$
2	Converse	$\text{If }n>-3,\text{ then}-2n<6$	True, $\begin{array}{l}n>-3\\ 2\times n>2\times \left(-3\right)\\ 2n>-6\\ -2n<6\end{array}$
3	Inverse	$\text{If }-2n>6,\text{ then }n<-3$	True, $\begin{array}{l}-2n>6\\ -n>3\\ n<-3\end{array}$