Prove the following statement. If R is any symmetric relation on a set A, then R -1 is symmetric. Some of the sentences in the following scrambled list can be used in a proof. By definition of R and since x R-1 y, then y Rx. By definition of R-1 and since x R y, then y RT 1 By definition of R-1 and since y R-1 x, then x R y. By definition of R-1 and since y R x, then x RT -1 y. 3. Since R is symmetric and y R x, then x R y. 4. ---Select--- X. Proof: We construct a proof by selecting appropriate sentences from the list and inserting them in the spaces. Construct the proof by using the appropriate statements from the list and putting them in the correct order. 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that x R¹ y. 2. ---Select--- 5. Therefore, by definition of a symmetric relation, R 1 is symmetric.

DISCRETE MATH Question 1: Let A be the set of all statement forms in the three variables p, q, and r, and let R be the relation defined on A as follows: For all S and T in A,  S R T  ⇔  S and T have the same truth table.   What are the distinct equivalence classes of R?   Thus, there are ________  distinct equivalence classes.    Question 2: There are as many equivalence classes as there are which of the following? (Select all that apply.) a. distinct real numbers b. distinct horizontal lines in the plane c. distinct integers d. distinct lines in the plane whose coordinates equal each other e. distinct vertical lines in the plane