For a sequence of sets A n, prove the following relation: lim inf A n C lim sup A„. Let S consist of all integers from 1 to 50. Define the following subsets of S: E x, all integers divisible by 5; E2,...

For a sequence of sets A n, prove the following relation:

lim inf A n C lim sup A„.

Let S consist of all integers from 1 to 50. Define the following subsets

of S: E x, all integers divisible by 5; E2, all integers divisible by 7; £ 3,

all odd integers less than 36. Find each of the following sets.

(a) E x D E2.

(b) £, n e 2 n £ 3.

(c) e x n e 2. _

(d) (£ , n e 2) n £3.

(e) (£ , - E2) n E 3.

(f) (£, - £ 3 ) n ( £2 - £ 3 ) .

(g) (£1 n £ 3) u j £ 2 n £ 3).

(h) E x n (£ 2 U £3).