1.
We say that a relation \(R\) on a set \(X\) is symmetric if \((x,y)\in R\) implies \((y,x)\in R\) for all \(x,y\in X\text{.}\) If \(X=\{a,b,c,d,e,f\}\text{,}\) how many symmetric relations are there on \(X\text{?}\) How many of these are reflexive?