Inference Rule with Quantifier and implication

[master cherundo]

Homework Statement

All healthy food does not taste good. "
Spinach is a healthy food. Duncan only want to eat tasty food. Duncan does not eat spinach. Hamburger is not a healthy food.
Write all possible conclusion.
I try to translate it into proposition with quantifier, such as $$t(x)=$$x is tasty, $$h(x)=$$x is healthy, $$d(x)=$$ Doddy eats x.

The Attempt at a Solution

I think $$d(hamburger)$$ is not a conclusion because the argument is $$d(x) \rightarrow t(x)$$. We cannot conclude $$d(hamburger)$$ or $$t(hamburger)$$, because proposition said $$h(x) \rightarrow ~t(x)$$ and $$d(x) \rightarrow t(x)$$. Is it right?

 

[HallsofIvy]

Yes, that is correct. (Assuming that "Doddy" is a nickname for "Duncan"!) Saying "All healthy food does not taste good" does NOT imply that unhealthy food does taste good. Of course, "not d(spinach)" would be a conclusion from the first two statements but that is given as the third statement.

 

[Architeuthis Dux]

Yes, your translation and reasoning are correct. The given argument does not provide enough information to conclude whether or not Duncan will eat a hamburger. The only conclusion that can be made is that Duncan will not eat spinach, as stated in the argument.