Set theory and relations - Is this relation symmetric, antisymetric or neither?

Question

I have just started learning set theory and need an explanation on how to go about this question:

Is the relation, "$xRy$ if and only if the difference of $x$ and $y$ is $<4$ " symmetric, antisymetric or neither?

Thanks in advance.

Answer 1

Guide:

Try to answer the following question:

• if the difference between $x$ and $y$ is less than $4$, can you say that the difference between $y$ and $x$ is less than $4$?

• if the difference between $x$ and $y$ is less than $4$ and the difference between $y$ and $x$ is less than $4$, can you conclude that $x=y$?

If the answer is yes, give a proof. If not, give a counter example.