SOLUTION: . 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

Algebra ->  Testmodule -> SOLUTION: . 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       Log On


   

Question 474977: . 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 plays football and Michael does not play basketball.

~p q
~p ~q
~(p q)
~(p ~q)


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
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 doesNOTplays+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 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).