i have $A$=$\left \{1,2,3,4,5,6 \right \}$ $R= \left \{ (a,b)|a\in A, b\in P(A),a\in b \right \}$ and i want to answer about what properties does this relation has, my Dilemma is about transentive and symmetry
Note: in my course antisimmetric property is defined as followed:regular antisemmetric :=$(a,b)\in R \Rightarrow (b,a)\not\in R$ Wide antisemmetric:= $(a,b),(b,a) \in R \Rightarrow a=b $
I need to distinguish between element and a set of element right? how it's effect symmetry property and transitive property
I conculeded : R is not semmetric beacuse $1R\left \{ 1,2 \right \} but \left \{ 1,2 \right \} \not R 1 $ and it is not Reflexive infect it is anti-Reflexive beacuse $\forall a \in A (a,a)\not \in R$ but i awere that this is problematic beacue $\left \{ 1,2 \right \} \not \in A$
Thank you.