1
$\begingroup$

where $2^N$ is the power set with $n$ elements (subsets).

Does it hold true to any set or just the power set $2^N$?

  • 0
    actually i was wondering if it were true on the power set 2^n.2012-11-22

1 Answers 1

3

By definition, two sets $A$ and $B$ are equal if and only if $A\subseteq B$ and $B\subseteq A$. Now a relation $R$ on a set $X$ is antisymmetric if $aRb$ and $bRa$ implies $a=b$ for all $a,b\in X$. Does this help you see why $\subseteq$ is antisymmetric?

  • 0
    yes, it is. The subset relation is antisymmetric because of the definition of set equality. This is true for all sets, so it is true for the power set of a set.2012-11-22