SOLUTION: Is the following relation a reflexive relation or not? Explain. A={(x,y)∈RXR:x is less than or equal to y} where R is the set of real numbers.

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Question 1126782: Is the following relation a reflexive relation or not? Explain.
A={(x,y)∈RXR:x is less than or equal to y} where R is the set of real numbers.
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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In order for to make all things clear, let me to explain you what is written in your post (to avoid misunderstanding). 

    You are given the set of all real numbers R.

    You consider all the pairs (x,y) of real numbers such that  x <= y. It is your set A.

    The set A  is not  a primary set of the consideration.

    The primary set is R.


    And the question is:  IS IT TRUE THAT FOR EVERY x from R  the pair (x,x)  is in the relation A, i.e.  x <= x  ??


Now I am ready to answer. 


This relation is reflexive.


To check it, you should make sure that for every real number x, the pair (x,x) is the relation.


In the terms of the given relation, it means to check that 



    for each real x,  x <= x.



but it is clearly and obviously true for all real numbers.

Answered and proved.


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If you have difficulties in understanding this issue, look into this Wikipedia article

https://en.wikipedia.org/wiki/Reflexive_relation