Evaluated Problems-
1. (Sundstrom) Consider the following relation R defined on Z.
xRy if and only if 3|(x+y).
Prove or disprove:
a) R is reflexive.
b) R is symmetric.
c) R is transitive.
d) R is an equivalence relation.
2. Consider the following relation ~ defined on R x R.
(x, y) ~ (a, b) if and only if (x - a) and (y - b) are integers.
Prove or disprove:
a) ~ is reflexive.
b) ~ is symmetric.
c) ~ is transitive.
d) ~ is an equivalence relation.
3. Explain why there is only relation on ∅. Then prove or disprove:
a) The relation is reflexive.
b) The relation is symmetric.
c) The relation is transitive.
d) The relation is equivalence relation.