tanisha does not own a convertible can be represented by ~p.
joan does not own a volvo can be represented by ~q.
~p means not p.
if p is true then ~p is false.
if p is false then ~p is true.
in this case ~p is true which means that p is false.
tanisha does not own a convertible is true which means that tanisha owns a convertible is false.
you do not need p or q in this analysis because they are not pertinent to the (~p or ~q) compound statement.
(~p or ~q) means that tanisha does not own a convertible or joan does not own a volvo.
(~p or ~q) is true in all cases except where ~p and ~q are both false.
The truth table shows that below:
~p ~q (~p v ~q)
T T T
T F T
F T T
F F F