Question

Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the compound statements into symbols. It is not the case that Jim does not play football or Michael plays basketball. (
~p V q
~(~p V q)
~(~p ^q)
~(~p ^ ~q)

Answer 1

~(~p V q)

Answer 2

p: Jim plays football
q: Michael plays basketball

So

~p: Jim does not play football

This then means that the statement "Jim does not play football or Michael plays basketball" translates to ~p V q

Finally, that first piece "It is not the case that" negates the whole thing to get the final answer of

~(~p V q)


So the answer is choice B