Topology

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Operations on Relations

TOPO-JGWZPH

Let $X$ and $Y$ be two sets, $R$ is a relation between $X$ and $Y$, and $F$ is a map from $X$ to $Y$.

Which of the following statements are TRUE?

Select ALL that apply.

A

$R\cup F$ is always a map from $X$ to $Y$.

B

If $R\neq F$ then $R\cap F$ can not be a map from $X$ to $Y$.

C

$R\cup F$ is a map from $X$ to $Y$ if and only if $R\subset F$.

D

If $R\cap F$ is non-empty, there is a non-empty sebset $X'\subset X$, such that $R\cap F|_{X'}$ is a map.