propositions - 2

[logistic_guy]

Let $\displaystyle p$ and $\displaystyle q$ be the propositions
$\displaystyle p$ : You drive over 65 miles per hour.
$\displaystyle q$ : You get a speeding ticket.

Write these propositions using $\displaystyle p$ and $\displaystyle q$ and logical connectives (including negations).

$\displaystyle \bold{(a)}$ You do not drive over $\displaystyle 65$ miles per hour.
$\displaystyle \bold{(b)}$ You drive over $\displaystyle 65$ miles per hour, but you do not get a speeding ticket.
$\displaystyle \bold{(c)}$ You will get a speeding ticket if you drive over $\displaystyle 65$ miles per hour.
$\displaystyle \bold{(d)}$ If you do not drive over $\displaystyle 65$ miles per hour, then you will not get a speeding ticket.
$\displaystyle \bold{(e)}$ Driving over $\displaystyle 65$ miles per hour is sufficient for getting a speeding ticket.
$\displaystyle \bold{(f)}$ You get a speeding ticket, but you do not drive over $\displaystyle 65$ miles per hour.
$\displaystyle \bold{(g)}$ Whenever you get a speeding ticket, you are driving over $\displaystyle 65$ miles per hour.

 

[logistic_guy]

$\displaystyle \bold{(a)}$ You do not drive over $\displaystyle 65$ miles per hour.

$\displaystyle \overline{p}$

 

[khansaheb]

$\displaystyle \bold{(a)}$ You do not drive over $\displaystyle 65$ miles per hour.

$\displaystyle \overline{p}$

Incorrect - the speed limit could be 55 MPh - it could even be 20 MPh.

 

[logistic_guy]

Incorrect - the speed limit could be 55 MPh - it could even be 20 MPh.

Take it easy man. Life is beautiful.

$\displaystyle \bold{(b)}$ You drive over $\displaystyle 65$ miles per hour, but you do not get a speeding ticket.

$\displaystyle p \land \overline{q}$

 

[logistic_guy]

$\displaystyle \bold{(c)}$ You will get a speeding ticket if you drive over $\displaystyle 65$ miles per hour.

$\displaystyle p \rightarrow q$

 

[logistic_guy]

$\displaystyle \bold{(d)}$ If you do not drive over $\displaystyle 65$ miles per hour, then you will not get a speeding ticket.

$\displaystyle \overline{p} \rightarrow \overline{q}$

 

[pka]

$\displaystyle \bold{(d)}$ If you do not drive over $\displaystyle 65$ miles per hour, then you will not get a speeding ticket.

$\displaystyle \overline{p} \rightarrow \overline{q}$

Yes that may work for your course
I would expect $\neg p \rightarrow \neg q$

 

[logistic_guy]

Yes that may work for your course
I would expect $\neg p \rightarrow \neg q$

Not when the author is Russian.

$\displaystyle \bold{(e)}$ Driving over $\displaystyle 65$ miles per hour is sufficient for getting a speeding ticket.

$\displaystyle p \rightarrow q$

 

[logistic_guy]

$\displaystyle \bold{(f)}$ You get a speeding ticket, but you do not drive over $\displaystyle 65$ miles per hour.

$\displaystyle q \land \overline{p}$

 

[logistic_guy]

$\displaystyle \bold{(g)}$ Whenever you get a speeding ticket, you are driving over $\displaystyle 65$ miles per hour.

$\displaystyle q \rightarrow p$