Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the compound statements into symbols.
Jim does not play football or Michael plays basketball.
1. p q
2. ~p q
3. p q
4. ~(p q)
To convert the compound statements into symbols, we can use the following symbols:
p: Jim plays football
q: Michael plays basketball
Now let's convert the compound statements:
1. Jim does not play football or Michael plays basketball.
This statement can be represented as "not p or q".
Symbolically, it can be written as "~p or q".
2. It is not the case that Jim plays football and Michael plays basketball.
This statement can be represented as "not (p and q)".
Symbolically, it can be written as "~(p and q)".
3. If Jim plays football, then Michael plays basketball.
This statement can be represented as "p implies q".
Symbolically, it can be written as "p -> q".
4. It is not the case that both Jim plays football and Michael plays basketball.
This statement can be represented as "not (p and q)".
Symbolically, it can be written as "~(p and q)".
Hint:
(p : Jim plays football)
~p : Jim does not play football
q : Michael plays basketball.