If you have two separate relations, $S$ and $R$, on a common set $A$ and $S \subseteq R$
a.) is R reflexive if S is.
b.) is S antisymmetric if R is.
c.) is R transitive if S is.
Wouldn't these all be true because $S$ is a subset of $R$?
two different relations on a common set question (discrete)
0
$\begingroup$
discrete-mathematics
elementary-set-theory
1 Answers
0
$(a)$ and $(b)$ would be true.
For $(c)$, let's consider $A=\{x,y,z\}$, $S=\{(x,x),(y,y),(z,z)\}$ and $R=S\cup \{(x,y),(y,z)\}$. $S$ is clearly transitive, but $R$ isn't.