Chapter 6, Problem 5CT

Solution

(a)

To Write: the inverse of the statement “if point P is on AB, then $\overrightarrow{AB}\text{ >}\overrightarrow{AP}$ ”.

“if point P is not on AB, then $\overrightarrow{AB}\text{ is not greater than}\overrightarrow{AP}$ ”.

Given:

Statement is.

“if point P is on AB, then $\overrightarrow{AB}\text{ >}\overrightarrow{AP}$ ”.

Calculation:

Inverse of the statement is.

“if point P is not on AB, then $\overrightarrow{AB}\text{ is not greater than}\overrightarrow{AP}$ ”.

(b)

To Write: the contrapositive of the statement “if point P is on AB, then $\overrightarrow{AB}\text{ >}\overrightarrow{AP}$ ”.

if $\overrightarrow{AB}\text{ is not greater than}\overrightarrow{AP}$ , then point P does not on AB”.

Given:

Statement is.

“if point P is on AB, then $\overrightarrow{AB}\text{ >}\overrightarrow{AP}$ ”.

Calculation:

Contrapositive of the statement is.

if $\overrightarrow{AB}\text{ is not greater than}\overrightarrow{AP}$ , then point P does not on AB”.