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Abstract Algebra

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Relations on a Set: Symmetric Relations

ABSALG-EHQ2R4

Which of the following relations determined by $R\subseteq S\times S$ are NOT symmetric?

Select ALL that apply.

A

The relation $(s,t)\in R$ if and only if $s< t$ on the set $S$ of positive integers.

B

The relation $(s,t)\in R$ if and only if $t=\sqrt{s^2}$ on the set $S$ of positive integers.

C

The relation $(s,t)\in R$ if and only if $t$ is the daughter of the mother of $s$ on the set $S$ of $3$ elements consisting of a mother (who has only one sister), together with the mother's two only daughters.

D

The relation $(s,t)\in R$ if and only if $s$ has heard of $t$ on the set $S$ of all people, living or dead.

E

The relation $(s,t)\in R$ if and only if $s$ is the sister of $t$ on any set $S$ of female people.