Question

If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then

• A. $R\subset S$
• B. $S\subset R$
• C. $R=S$
• D. none of these

Answer 1

Answer: (B)

$S\subset R$

$S$ is a subset of $R$

Since $R$ is the largest equivalence relation on set $A$,

$R$ is a subset of $A\times A$

Since $S$ is any relation $A$

$S$ is contained in $R$

and $R$ is a subset of $a\times A$

So, $S\subset R$