  Extremal problems involving independent sets are much studied. Two of the
most important extremal problems in this context are concerned with the sharp
upper bounds for the number of independent sets of fixed size and the
independence number. In literature, these sharp upper bounds are derived in
completely different contexts. In this paper, we show that both of these sharp
upper bounds can be derived by considering Lex graphs. More exactly, they
depend on two parameters of a sequence defined on them.
