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 pl

Algebra ->  Conjunction -> 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 pl      Log On


   

Question 435503: 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.
(Multiple Choice)
A.) ~p Λ q
B.) ~p Λ ~q
C.) ~(p Λ q)
D.) ~(p Λ ~q)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Unfortunately there are no parentheses and without them the statement
is ambiguous

If it is to be taken this way:

It is not the case that (Jim plays football and Michael does not play
basketball)

then the answer is 

~(p /\ ~q)  choice D.

However if it is to be taken this way:

(It is not the case that Jim plays football) and Michael does not play
basketball

then it would be 

~p /\ ~q   choice B

But I would guess it would be D because if he had meant B it would
have been worded this way:

Jim does not play football and Michael does not play basketball.

So I would go with D.  But there is no reason to assume that
"it is not the case that" applies to the conjunction and not just
to the first statement only.   You might point out this ambiguity 
to your teacher.

Edwin