Answer to Question #311006 in Real Analysis for Dhruv rawat

Question

Show that the set

X= [1,5]U[6,9]U[15,30] is an compact subset of R

Answer 1

A closed interval [a,b] is a closed subset of R. The finite union of closed sets is closed set. Hence X is closed set.

X is bounded since $|x|\leq 30, x\in X$ .

By the criterion of compactness in R, X is compact.