Answer
a)
Converse= if it will drive to work, then it rains today.
Contrapositive= if I will not drive to work then it does not rain today
Inverse= if it does not rain today, then I will not drive to work.
b)
Converse=If $x \geq 0$ , then $|x|=x$
Contrapositive=If $x<0,$ then $|x| \neq x$
Inverse= If $|x| \neq x,$ then $x<0$
c)
Converse= if $n^{2}$ is greater than $9$, then $n$ is greater than $3$.
Contrapositive= if $n^{2}$ is not greater than $9$, then $n$ is not greater than $3$.
Inverse: if n is not greater than $3$, then $n^{2}$ is not greater than $9$.
Work Step by Step
a) The given statement is of the form $p→q$ with
$p$= “it rains today”
$ q$= “I will drive to work”
converse, contrapositive and the inverse of the given conditional statement:
Converse= if it will drive to work, then it rains today.
Contrapositive= if I will not drive to work then it does not rain today
Inverse= if it does not rain today, then I will not drive to work.
b) This statement is also of the form $p→q$ with
$p$= $|x|=x$
$q$= $x \geq 0$
converse, contrapositive and the inverse of the
given conditional statement:
Converse=If $x \geq 0$ , then $|x|=x$
Contrapositive=If $x<0,$ then $|x| \neq x$
Inverse= If $|x| \neq x,$ then $x<0$
c) The statement is of the form $p→q$
$p$= $n^{2}$ is greater than $3$.
$q$=$n$ is greater than $9$
Converse= if $n^{2}$ is greater than $9$, then $n$ is greater than $3$.
Contrapositive= if $n^{2}$ is not greater than $9$, then $n$ is not greater than $3$.
Inverse: if n is not greater than $3$, then $n^{2}$ is not greater than $9$.
