Q: Let S = {x, y, z } and R is a relation defined on S such that
R={(y,y),(x,z),(z,x),(x,x),(z,z),(x,y),(y,x)}
Show that R is reflexive and symmetric as well.
Since R is finite, you can easily check this by brute force. R is reflexive because (x,x), (y,y), and (z,z) are in R.
For symmetry: Since (x,z) is in R, we also need (z,x) in R. Is it? Yes it is. Similarly, since (x,y) is in R, we need (y,x) in R, and indeed, it is.