Show that the inclusion relation, $\{ ( A , B ) \mid A \subseteq B \}$ , is a partial ordering on the set of all subsets of $\mathbf { Z }$

Question

Quizplus · Accepted Answer

The Answer is We see that set inclusion is reflexive since A

\subseteq

A whenever A is a subset of

\mathbf { Z }

. Since A

\subseteq

B and B

\subseteq

A imply that A=B whenever A and B are subsets of Z , we see that set inclusion is antisymmetric. Now suppose that A

\subseteq

B and B

\subseteq

C where A, B , and C are subsets of

ext { Z }

Then A

\subseteq

C , so set inclusion is transitive.

Show That the Inclusion Relation {(A,B)∣A⊆B}\{ ( A , B ) \mid A \subseteq B \}{(A,B)∣A⊆B}