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.

\(\displaystyle p \rightarrow q\)