Subset Relations

fg9

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When "A" is a subset of "B", is the relation "antisymmetric", "transitive" or "reflexive"?
 

pka

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When "A" is a subset of "B", is the relation "antisymmetric", "transitive" or "reflexive"?
In set theory we use \(A\mathcal{R} B\) to read \(A\) is related to \(B\) or in this case \(A\subseteq B\)
1) If \(A\mathcal{R} B~\&~B\mathcal{R} A\) does that mean \(A= B~?\) If so the it is antisymmetric.
2) If \(A\mathcal{R} B~\&~B\mathcal{R} C\) does that mean that \(A\mathcal{R} C~?\) If so the it is transitive.
3) If for each set \(A\mathcal{R} A\) then it is reflexive.
 
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