Let a b be a closed interval on the real line and c d an ope

Let [a, b] be a closed interval on the real line, and (c, d) an open interval which is a subset of [a, b]. Prove that the closed interval [c, d] is also a subset of [a, b].

Solution

Closure of (c,d)=[c,d] which is the smallest closed set containing (c,d)

But, (c,d) is contained in [a,b]

HEnce,[c,d] is contained in [a,b]