Prove or disprove the relation is reflexive and symmetric

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Reference no: EM131047984

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.

Reference no: EM131047984

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