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Abstract Algebra

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Relations on a Set: Reflexive Relations

ABSALG-K5BZXE

Which of the following relations determined by $R\subseteq S\times S$ is "reflexive"?

Select ALL that apply.

A

the relation $(s,t)\in R$ if and only if $s\preceq t$ on a set $S$ with a partial order $\preceq$

B

the relation $(s,t)\in R$ if and only if $s^3=t^4$ on the set $S$ of positive integers

C

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

D

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

E

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