1. Let S be the Cartesian coordinate plane R × R and define the equivalence relation R on S by (a, b) R (c, d ) iff b – 3a = d – 3c. (a) Find the partition p determined by R by describing the pieces...

1. Let S be the Cartesian coordinate plane R × R and define the equivalence relation R on S by (a, b) R (c, d ) iff b – 3a = d – 3c.

(a) Find the partition p determined by R by describing the pieces in p .

(b) Describe the piece of the partition that contains the point (2, 5).

2. Let R be the relation {(1, 1), (2, 3), (2, 2), (3, 2), (3, 3)} on the set {1, 2, 3}. Determine whether or not R is an equivalence relation. If it is not, state which properties it is lacking. If it is, describe the partition p determined by R by listing the pieces in