Unit 21 Answers
1.
a) Equivalence relation
b) Equivalence relation
c) Not symmetric, not transitive
2.
3. Let R = { (p, q) | p q and p and q are propositions }. A proposition p is equivalent to q means that p and q always have the same truth value. Since p has the same truth value as p, R is reflexive. R is symmetric, since if p and q have the same truth value, then q and p have the same truth value. If p and q have the same truth value and q and r have the same truth value, then p and r also have the same truth value. So R is transitive. Hence R is an equivalence relation.
4. { 6n + k | n Z } for k {0, 1, 2, 3, 4, 5}, where Z is the set of integers.
5. a) No b) Yes c) No d) Yes
6. a) The set of integers b) {n + 0.3 | n Z}