Thread: Which relations are reflexive

Which of the following relations are reflexive

1) x~y if and only if x-y is a multiple of 10
2) x~y if and only if xy >= 0
3) x~y if and only if x - y is positive
4) x~y if and only if x+y is odd
5) x~y if and only if x+y is positive

I know the definition of reflexixe is xRx but i dont really understand how to apply it

Thanks

Well, let's start from the beginning. First, you need to know how to substitute a concrete expression for a variable in another expression. Here are a few exercises. Please write the answers.

(1) Substitute 2 for x (i.e., replace x with 2) in x + 2 = 4.
(2) Substitute (3 + 5) for y in (y + 1)² = y² + 2y + 1. Don't do any simplification; just do the substitution.
(3) Let the function f(x) be defines as x + 1. Replace f with its definition in f(y + 2) + f(y + 3) = 2y + 7. Again, don't do any simplification.
(4) Let the relation R(x,y) be defines as x < y and let U(x,y) be defined as x ≤ y. Replace R and U with their definitions in "R(x,y + 1) if and only if U(x,y)."

Second, you need correct definitions.

Originally Posted by hampsterbones

I know the definition of reflexixe is xRx

This resembles the correct definition, but it's so sloppy that it's not a definition at all. Write the correct, precise definition of "reflexive." Be sure to consult the source (textbook or lecture notes). The definition should start with "A binary relation R on a set A is reflexive if ..." Note that your original question lacks some information because it does not say on which set we consider those relations.