Limit Proofs (Sup and Inf)

please show and explain

a. B = lim sup An = {w : w element An for infinite many values of n}

and C = lim inf An {w:w element An for all but finitely many values of n}

b. Let (X, F, P) be the probabilty space with X = (0, 1), F the Borel sets and P the uniform distribution. Let An = (1/2 + 1/n, 1 - (1/n))

Calculate Cn, Bn, lim sup n--> infite An and lim inf n --> infinity An. Does A = lim n--> infitite exist? If so, what is P(A)?

c. Let An = (0,(1/2) - (1-n)) if n is odd

((1/2), 1 - (1-n) if n is even

again calculate Cn, Bn, lim sup n -->inifinity An and lim inf n-->infinity An. Does lim n --> infinity An exist? If so, what is P(A)?