# Inference Rule with Quantifier and implication

1. Oct 14, 2008

### master cherundo

1. The problem statement, all variables and given/known data
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.

3. 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?

2. Oct 15, 2008

### HallsofIvy

Staff Emeritus
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.