List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric.

List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric

Discrete Math : Let R be a symmetric relation show that R to the power n is symmetric for all positive integers n.

Let R be a symmetric relation show that R to the power n is symmetric for all positive integers n.

Discrete Math : Show that the symmetric closure of the union of 2 relations is the union of their symmetric closures.

Show that the symmetric closure of the union of 2 relations is the union of their symmetric closures.

Relations : A relation R is called circular if a R b and b R c imply that c R a. Show that R is reflexive and circular if and only if it is an equivalence relation.

A relation R is called circular if a R b and b R c imply that c R a. Show that R is reflexive and circular if and only if it is an equivalence relation.

Discrete mathematics

Find a transitive closure of the relation R on {a,b,c,d,e} given by R= {(a,b), (a,c), (a,e),(b,a), (b,c),(c,a), (c,b),(d,a,),(e,d)}