SOLUTION: Write the compound statement in words. p = The puppy behaves well. q = His owners are happy. ~(p -> q) which one is correct I'm confussed. 1) It is not the case that if the pu

Question 465848: Write the compound statement in words.
p = The puppy behaves well.
q = His owners are happy.
~(p -> q)
which one is correct I'm confussed.
1) It is not the case that if the puppy behaves well then his owners are happy.
2) The puppy does not behave well or his owners are happy.
3) If the puppy does not behave well then his owners are not happy.
4) It is not the case that the puppy behaves well if his owners are not happy.
( I think it is 3 but I'm not sure.)
Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
p -> q means: If the puppy behaves well, then his owners are happy.
~(p -> q) negates the WHOLE THING all at once--don't distribute the "not", just leave it out front. Without looking at answer choices, I'd say something like "NOT TRUE: If the puppy behaves well, then his owners are happy." That is what 1 says.

3, which is what you were thinking, would look like ~p -> ~q. As much as it seems like we could have distributed the not (~), it's not legal in logic.
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