1
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2answers
38 views

How to show properties of a given relation?

I am given that R is a relation on the given set X, and I have to show if the relation is (i) reflexive, (ii) symmetric, (iii) transitive, (iv) asymmetric, and (v) give an example of an element of ...
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0answers
12 views

Name for symmetric irreflexive binary relation

I have an irreflexive relation $\prec$ called unpreference: if $x\prec y$ then I say $x$ is unpreferred (or not preferred) to $y$. I wish to give a name to the symmetric part of the relationship, ...
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1answer
28 views

Prove the following $R \subseteq A\times B$ and $S\subseteq B\times C \rightarrow $ $ S \circ R $ is symetric

I want to prove the following $ S \circ R $ is symetric, A,B, C are sets $R \subseteq A\times B$ is Symetric $S\subseteq B\times C$ is Symetric Any Suggestions? Thanks!
1
vote
1answer
222 views

Proving the symmetry of an equivalence relation

When proving the symmetry of an equivalence relation, must each equivalence class be closed under symmetry. for example: the relation both x and y > 10 or both x and y < 10 across all ...
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votes
2answers
669 views

Proving symmetry of Relation and Inverse Relation

Why is this a flawed proof? Knowing that $a$ is an element in $A$ and $b$ is an element in $B$. $R$ being a symmetric binary relation: “Consider any $a$ and $b$ such that $aRb$. Since $R$ is ...
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1answer
597 views

How can this relation be anti-symmetric and symmetric at the same time?

Why is this anti-symmetrical and symmetrical at the same time? I get how it is anti-symmetric because There is no pair such as (1,2) & (2,1) but how did it become symmetrical? ...