Let R and S be two equivalence relations on a set A. Define T and U as: xTy ⇐⇒ xRy ∧ xSy, xUy ⇐⇒ xRy ∨ xSy,
A. Show that T is an equivalence relation.
B. Show that U is not necessarily an equivalence relation (i.e. for some choices of R, S, we have that U is not an equivalence relation)