Let $A$ be nonempty set, check whether $\subseteq$ is a partial order on $P(A)$.

Question

How can I show that this is a partial order? did not really help because I got confused

I found it to be
*Transitive since if $A\subseteq A$ and $A\subseteq B$ then $A\subseteq B$
*Antisymmetric since $A\subseteq A$ and $A\subseteq A$ so $A=A$
*Reflective since $A\subseteq A$ and $A\subseteq A$

But I am not sure if my way of solving this or the answer is whether true or not, can anyone confirm?

score 0 · Answer 1 · answered Oct 29 '17 at 19:34

0

You are suppose to consider elements $B,C,D \in P(A)$ and verify those properties.

For example for transitive, you are suppose to check

if $B \subseteq C$ and $C \subseteq D$, whether we have $B \subseteq D$.

answered Oct 29 '17 at 19:34

Siong Thye Goh

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So I have to say A⊆B and B⊆C then A⊆C? – Chaul Oct 29 '17 at 19:35
well, try to avoid using the notation $A$ again because in this question, $A$ is a special set that is used to construct $P(A)$. – Siong Thye Goh Oct 29 '17 at 19:40

Let $A$ be nonempty set, check whether $\subseteq$ is a partial order on $P(A)$.

1 Answers1