- #1

- 479

- 12

## Homework Statement

I refer to part G of this little problem:

I don't see how to arrive at any conclusion, especially when I can't even see how ##z## comes into play. Assistance in interpreting the problem is appreciated!

## Homework Equations

## The Attempt at a Solution

I know that the answer for G is "False", which means I have to show that the following is true;

$$\exists x \in A, \ \forall y \in A, \exists z \in A, \ \neg P(x,y) \lor \neg P(y,z)$$

Here's how I have tried to interpret the problem.

$$\neg P(x,y) \lor \neg P(y,z)$$

is true when either or both predicates are false. Looking at a particular ##x## and all combinations of ##y## that come with it (##\exists x \in A, \ \forall y \in A##), none of them are able to make ##P(x,y)## false all the time.

So now I try to look at all ##y## (that are already paired with some ##x##) and try to find some ##z## for each of the ##y## that would cause ##p(z,y)## to always be false. However, I'm not sure where and how to apply the ##z## since it's not defined in the table.

Was this how I am supposed to interpret the problem? Apologies if what I have written is unintelligible as I am finding logic rather confusing.