Let A 1n 2n n 1 2 3 and B x elementof Q 0 Solutiona Lim

Let A = {(-1)^n + 2/n: n = 1, 2, 3, ...} and B = {x elementof Q: 0

Solution

(a) Limit points of set A are all the irrational and ration points in (-1,0)U(1,2) which are not present in A and limit points of set B are all the irrational points in (0,1).

(b) Set A is open set and set B is closed set.

(c) Set A contains isolated points, but set B does not contain any isolated points.

(d) Closure of A is (-1,0)U[1,2] and close of B is (0,1)