# How to Interpret the Basic Logic Problem with Predicate P(x,y,z)

• WWCY
In summary: The table of truth of P(y,z) is the same as table of truth for P(x,y) with two differences: where x you put y and where y you put z.This is all very confusing and I need some help to figure this out. the table of truth of P(y,z) is the same as table of truth for P(x,y) with two differences: where x you put y and where y you put z.I see the table I tried to make using standard text editing doesn't look that good but I think you ll understand it. for example it is P(y,z)=T for y=0 and z=0, P(
WWCY

## 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!

## 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.

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the table of truth of P(y,z) is the same as table of truth for P(x,y) with two differences: where x you put y and where y you put z.
that is it is
y 0 1 2
z \
0 T F T
1 T T F
2 T F F​

I see the table I tried to make using standard text editing doesn't look that good but I think you ll understand it. for example it is P(y,z)=T for y=0 and z=0, P(y,z)=F for y=1 and z=0, P(y,z)=T for y=2 and z=0...

WWCY
WWCY said:

## Homework Statement

I refer to part G of this little problem:

View attachment 230498

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!

## 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)##
...
Don't be fixated on what variable name is used for a particular index (parameter) .

For example: If we set x = 0 and y = 1, then P(x,y) is True. However P(y,x) is False for the same choices of x and y, because this is P(1,0) .

WWCY and Delta2

## 1. What is a Basic Logic Problem?

A Basic Logic Problem is a type of mathematical puzzle that involves using logical reasoning to solve a problem. It typically consists of a set of clues or statements, and the goal is to use deductive reasoning to determine the correct solution.

## 2. How do you solve a Basic Logic Problem?

The first step in solving a Basic Logic Problem is to carefully read and understand the given clues. Then, you can use logical reasoning to eliminate possibilities and narrow down the potential solutions. It is important to keep track of the information you have gathered and make deductions based on the clues provided.

## 3. What are the different types of Basic Logic Problems?

There are several types of Basic Logic Problems, such as grid puzzles, deductive reasoning puzzles, and syllogisms. Each type has its own unique set of rules and solving techniques.

## 4. Can Basic Logic Problems be solved using only logic and no outside knowledge?

Yes, Basic Logic Problems are designed to be solved using only logical reasoning and no outside knowledge or information. This makes them a fun and challenging exercise for the mind.

## 5. Are Basic Logic Problems useful in real-life situations?

While Basic Logic Problems may not have direct real-life applications, they can help improve critical thinking, problem-solving, and deductive reasoning skills, which can be useful in various situations, such as decision-making and analytical thinking.

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