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 d

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Question 260703: 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.
I am not getting this symbol stuff at all..Please help me.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let
p: Jim plays football
q: Michael plays basketball

So what this means is that wherever you see a 'p', it will essentially stand for "Jim plays football". Think of this as talking in code.

The symbol ~ stands for the negation of a given statement. So ~p means NOT p. It is the opposite of what p represents. So if p: Jim plays football, then ~p: Jim does NOT play football. You can see that p and ~p are opposites of each other.

Also, the symbol stands for "or"

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

So "Jim does not play football" translates to and "Michael plays basketball" translates to . Combine the two symbols with a to get (since we're dealing with an 'or' situation)

Finally, negate the entire statement by placing a outside the parenthesis to get . We're doing this because the beginning of the sentence states that "it is not the case" which means that we take the opposite of whatever the remaining sentence is claiming.

So the full translation of "It is not the case that Jim does not play football or Michael plays basketball" is