Question 474977
if

{{{p}}}: Jim plays football
{{{q}}}: Michael plays basketball


that means is that wherever you see a '{{{p}}}', it will stand for "{{{Jim}}} {{{plays}}}{{{ football}}}". 


The symbol ~ stands for the {{{negation}}} of a given statement. So ~{{{p}}} means {{{NOT}}}{{{ p}}}. 

 So if {{{p}}} means "{{{Jim}}} {{{plays}}}{{{ football}}}", then ~p: "{{{Jim}}} {{{does}}}{{{NOT}}}{{{plays}}}{{{ football}}}". 


Also, the symbol {{{V}}} stands for "{{{or}}}"


First, take a look at the statement "Jim does not play football or Michael plays basketball". We are going to ignore the beginning part "It is not the case" for now.


So "Jim does not play football" translates to  ~ {{{p}}} and "Michael plays basketball" translates to {{{q}}}. 

Combine the two symbols with a {{{V}}} to get ~ {{{p}}} {{{V}}} {{{q}}} (since we're dealing with an 'or' situation)



Finally, negate the entire statement by placing a *[Tex \LARGE \sim] outside the parenthesis to get ~(~ {{{p}}} {{{V}}} {{{q}}}), because the beginning of the sentence states that "it is not the case". 


So the full translation of "It is not the case that Jim does not play football or Michael plays basketball" is ~(~ {{{p}}} {{{V}}} {{{q}}}).