Let $p,q,$ and $r$ be the following propositions: $p$ : "You get an A on the final exam", $q$ : "You do every exercise in this book", and $r$ :"You get an A in this class.". Write the following statement using. $[0\mathrm{.}5$pt$]$

"You will get an A in this class if and only if you either do every exercise in this book and you get an A on the final."

a$)rharr{p}^{{?}^{?}}q$

b$)$ rharrnotpvvq

c$)$ notrharrpvvq

d$)$ notrharrnot$(pvvq)$

What is the contrapositive of the conditional statement $"$ The message is not scanned for viruses whenever the message was sent from a known system $"[0\mathrm{.}5$pt$]$

a$)$ If the message was not sent from a known system, then the message is scanned for viruses.

b$)$ If the message was sent from a known system, then the message is scanned for viruses.

c$)$ If the message is scanned for viruses, then the message was not sent from a known system.

d$)$ If the message is not scanned for viruses, then the message was sent from a known system.

What is the converse of the conditional statement $"$ The message is not scanned for viruses whenever the message was sent from a known system $"[0\mathrm{.}5$pt$]$

a$)$ If the message was not sent from a known system, then the message is scanned for viruses.

b$)$ If the message was sent from a known system, then the message is scanned for viruses.

c$)$ If the message is scanned for viruses, then the message was not sent from a known system.

d$)$ If the message is not scanned for viruses, then the message was sent from a known system.

What is the inverse of the conditional statement $"$ The message is not scanned for viruses whenever the message was sent from a known system" $[0\mathrm{.}5$pt$]$

a$)$ If the message was not sent from a known system, then the message is scanned for viruses.

b$)$ If the message was sent from a known system, then the message is scanned for viruses.

c$)$ If the message is scanned for viruses, then the message was not sent from a known system.

d$)$ If the message is not scanned for viruses, then the message was sent from a known system.

Determine whether this biconditional is true or false. $[0\mathrm{.}5$pt$]0^2>0$ if and only if

$\frac{T}{F}$

Determine whether this biconditional is true or false. $[0\mathrm{.}5$pt$]4+1=5$ if and only if $2$ is odd.

$\frac{T}{F}$

Determine whether this biconditional is true or false. $[0\mathrm{.}5$pt$]$

The sun is very cold if and only if there are $90$ minutes in one hour.

$\frac{T}{F}$