Can anyone give me some hints about this homework? I`m really stuck. Thank you.
Let R is a binary relation in A. Define T and S using R, such that S is the smallest symmetric relation which $R \subseteq S$ and T is the biggest symmetric relation which $T \subseteq R$. (In other words, S and T are binary relations, defined using the sets R,$\varnothing, Id_{A}, A \times$ A and the operations $\cup,\cap , \ ^{-1}, \circ $)