For each of the following relations, determine whether the relation is:

Reflexive. Anti-reflexive.

Symmetric. Anti-symmetric.

Transitive. A partial order.

A strict order. A total order.

An equivalence relation.

a. is a relation on the set {, , , } such that = {(, ), (, ), (, ), (, ), (, ), (, )}.

b. is a relation on the set of all people such that (, ) if and only if and have a common grandparent.

c. is a relation on the power set of a set such that (, ) if and only if .

d. is a relation on + such that (, ) if and only if there is a positive integer such that = .

e. is a relation on such that (, ) if and only if .