# Tagged Questions

For reflexive, symmetric and transitive relations. Use it with the tag (relations).

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### Proving the Binary Relation is an Equivalence Relation

Let $R$ be a binary relation on a set A and suppose R is symmetric and transitive. Prove the following: If for every $x$ in $A$ there is a $y$ in $A$ such that $x R y$, then $R$ is an equivalence ...
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### Finite group existence of equivalence relation

I was reading about cosets and, given the fact that if $H$ is a non empty subset of a finite group G, we have the following equality $[G:H]|H|=|G|$, I came up with the following question: If the ...
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### Proving a function $\mathbb{Z}_m \to \mathbb{Z}_m,\ [a] \mapsto [a^2 + 3a + 1]$ is well defined

Prove that $\operatorname{poly}\colon \mathbb{Z}_m \to \mathbb{Z}_m$ given by $\operatorname{poly}\colon [a] \mapsto [a^2 + 3a + 1]$ is well defined. This is what I have so far, working in (mod m) ...
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### Why is one relation transitive but the other is not?

From what I have read about a transitive relation is that if xRy and yRz are both true then xRz has to be true. I'm doing some practice problems and I'm a little confused with identifying a ...
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### 51 people enter a raffle with 10 prizes; 7 are pencils and 3 are cars. How may ways are there to give out the prizes?

Assume that no one can win more than one prize. If the prizes were all different, then we have the case that order matters and repeats are allowed, meaning there are $P(51, 10)$ ways of handing out ...
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### Equivalence relation and partitions [closed]

Define an equivalence relation on the set R that partitions the real line into subsets of length 1.
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### For each $x \in X$, $x/ \mathscr E=\{y \in X \mid y\mathscr Ex\}$? Shouldn't it be for each $y \in X$?

"Definition 6. Let $\mathscr E$ be an equivalence relation on a nonempty set $X$. For each $x \in X$, we define $x/ \mathscr E=\{y \in X \mid y\mathscr Ex\}$ which is called the equivalence ...