Suppose a is the set of all human beings and r is the relation xry iff x has lived in the same house as y.
this relation is:
reflexive only
reflexive and symmetric but not transtivie
reflexive and transitive but not symmetric
symmetric only
symmetric and transitive but not reflexive
transitive only
reflexive, symmetric and transitive
not reflexive, not symmetric and not transitive
3. on the set of all real numbers, the relation xry iff x < y is
reflexive only
symmetric only
transitive only
reflexive and symmetric but not transitive
reflexive and transitive but not symmetric
symmetric and transitive but not reflexive
neither reflexive, transitive, nor symmetric
an equivalence relation
4. on the set {a, c,e} define the relation r by {(ac)}. this relation
is an equivalence relation
is not an equivalence relation because it is not transitive
is not an equivalence relation because it is not symmetric
is not an equivalence relation because it is not reflexive
5. on the set of human beings, which of the following is an equivalence relation?
arb iff a loves b
arb iff a has seen b at wegmans
arb iff a graduated from the same high school as b
arb iff a has b's phone number
more than one of the given choices is an equivalence relation