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I am having some confusing regarding reflexive relations. Let's take an example $$\{(a,b):a+2b\ \text{must be divisible by 3, a and b are natural numbers}\}$$

Some elements of the relation are $(1,1),(2,2),(3,3), \cdots$ where $a = b$

But there are also some elements like $(1,4),(2,5),(5,10)$ etc. where $a \neq b$.

So would this relation be considered reflexive?

David Scholz
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Nipun Kulshreshtha
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  • The set is reflexive if it contains all the $(a,b): a=b$. Does it contain all of them? If it does it is reflexive. It doesn't matter if it contains more things. The only question you have to ask is does it contain all $(a,b):a=b$, that is, for any $a+2b$ where $a=b$ is $a+2b$ divisible by $3$? – fleablood Jan 25 '22 at 17:11

1 Answers1

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A reflexive relation on a set $X$ must contain ALL the pairs $(x,x)$ for $x \in X$.

That doesn't mean that it can't have more pairs that are not of that form.

jjagmath
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