covert the compound statement into words.
Let r="the food is good"
p="I eat too much"
q=I'll exercise."
I'll exercise if i don't eat to much.
1.~p^q
2.~(p->q)
3.~p->q
4.~p,q
To convert the compound statement into words, we need to understand the logical operators in play.
Given:
r = "the food is good"
p = "I eat too much"
q = "I'll exercise."
The compound statement is: I'll exercise if I don't eat too much.
Let's analyze the different options:
1. ~p^q:
This translates to "I don't eat too much and I'll exercise."
2. ~(p->q):
This translates to "I don't eat too much, but I won't exercise."
3. ~p->q:
This translates to "If I don't eat too much, then I'll exercise."
4. ~p, q:
This translates to "I don't eat too much, and I'll exercise."
Out of these options, the closest translation to the given compound statement is option 3: ~p->q.
rearrange to
(i don't eat too much) -> (I'll exercise)
~p -> q