Consider the binary relation for "less than" with the symbol <. This relation does not define an equivalence relation on the real numbers, but it does have some of the properties of an equivalence relation. Which properties does it have? (Hint: Consider 1 <2,2<3, etc.) O a. Reflexive and Symmetric. O b. Symmetric only. OC. Symmetric and Transitive. O d. Transitive only. O e. Reflexive and Transitive.

6. ((a, b), (c, d)) ER if and only if ad = bc. Show R is an equivalence relation. Let R be the relation on the set of ordered pairs of positive integers such that

5 Equivalence relation? A relation on the integers is divided by x~y if and only ifx+2y is divisible by 3. Is this an equivalence relation? If so, describe the equivalence classes of ~. If not, explain why not.

Let S be a nonempty set. Consider the relation ~ on P(S) defined by A ~ B if AUBC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of