Question

For each of the following relation on N, the of set positive integers, determine which of the five properties are satisfied.

R= x + y is odd

a. Reflexive
b. Irreflexive
c. Symmetric
d. Antisymmetric
e. Transitive

Answer 1

b. irreflexive

c. Symmetric

e. Transitive

Explanation:

For a positive integer, the variable can be Reflexive if it is to be independent and can complete the set on itself. For symmetric both variables can be interchangeable. For transitive both variables can display same function. In the given function both variables are odd, they are symmetric.