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.   Prove that R is an equivalence relation.  What are the distinct equivalence classes of R?

How many relations are there on the set {a, b, c, d}

prove why each relation has or does not have theproperties: reflexive, symmetric, anti-symmetric, transitive. 4) Z+ is the set of positive integers, relation R: Z+x Z+, a,b,c,d ∈ Z+; (a,b),(c,d) ∈ R if an only if   a + d = b + c.

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