# Determine if the following problem is symmetric and transitive

• Meager
In summary, ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. It is not symmetric or transitive, as it fails to hold for all numbers when tested with different values of a and b.
Meager

## Homework Statement

Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is
symmetric
transitive

ab2 must ba2

## The Attempt at a Solution

I tried using different numbers, but it isn't coming out as a perfect square.

For example, I said a=1
b=0........ Then this works.
Using other numbers it fails.

Should a=b?

Welcome to PF!

Hi Meager! Welcome to PF!
Meager said:
Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is
symmetric
transitive

Hint: write a and b as a product of their prime factors.

## 1. What does it mean for a problem to be symmetric?

Symmetry in a problem means that the relationship between two elements is unchanged when the order of those elements is reversed.

## 2. How can I determine if a problem is symmetric?

To determine if a problem is symmetric, you can check to see if switching the order of the elements in the problem results in the same outcome or relationship.

## 3. What does it mean for a problem to be transitive?

Transitivity in a problem means that if element A is related to element B and element B is related to element C, then element A is also related to element C.

## 4. Can a problem be both symmetric and transitive?

Yes, a problem can be both symmetric and transitive. This means that the relationship between elements in the problem is unchanged when the order is reversed, and the transitive property holds true for all elements in the problem.

## 5. Why is it important to determine if a problem is symmetric and transitive?

Determining if a problem is symmetric and transitive can help identify patterns and relationships between elements, which can aid in finding solutions or making predictions. It also ensures that the problem is logically consistent and can be applied in various situations.

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