CSCI 301, Math Exercises #3
1. Consider the relation | (divides) on the set Z. (a) Prove or disprove: | is reflexive. (b) Prove or disprove: | is symmetric. (c) Prove or disprove: | is transitive.
2. Assume R and S are two equivalence relations on a set A. (a) Prove or disprove: R∪S is reflexive. (b) Prove or disprove: R∪S is symmetric. (c) Prove or disprove: R∪S is transitive.
3. Consider the function θ : {0,1}×N→Z defined as θ(a,b) = a−2ab + b (a) Prove or disprove: θ is injective. (b) Prove or disprove: θ is surjective.
