# Questions tagged [relations]

For questions concerning partial orders, equivalence relations, properties of relations (transitive, symmetric, etc), a composition of relations, or anything else concerning a relation on a set.

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### Inverse Relation for Allocating an Amount

This question came up in the context of project finance. It is my original question. Quick Version A project has upfront cost $X$, and ongoing cost $Z$. (Z is less than X). There are the same $N$ ...
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### How to prove that $f$ inverse: $Y \to X$ is one-one and onto given that $f^{-1}:X \to Y$ is one-one and onto? [closed]

If $f:X \to Y$ is one-one and onto, then prove that $f^{-1}:Y \to X$ is also one-one and onto.
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### Why do we care about well-founded sets? [closed]

Well-founded sets are frequently studied in set theory. I wonder what are the motivations for caring about them ? We study them just for sake of curiosity or are there any reasons/problems/...
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### A relation coming both transitive and not transitive

A relation $R$ is defined as $(x,y)\in R \implies x^y=y^x$ for $x,y\in\mathbb{I}-\{0\}$, where $\mathbb{I}$ is the set of integers. Find whether the relation $R$ is transitive or not. Let $x^y=y^x$ ...
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### Can an equivalence relation contain the null set?

An arbitrary partition $F$, for some equivalence relation $R$, importantly does not contain any set $X$ such that $X = \emptyset$. However, is it possible for a constituent equivalence class, $[x]_R$ ...
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### Algebraic Proof that the Amplitude does not affect Frequency

In Simple Harmonic Motion, the Amplitude is defined as the maximum displacement. Consider a pendulum (SHM) or a mass on a horizontal or vertical spiring. If the amplitude increases, which means ...
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