Lebesgue measure of proper subset

Question

Is it true that if A is a proper subset of B, then the Lebesgue measure of A is strictly less than the Lebesgue measure of B?

Answer 1

No, take $[0,1]$ and $[0,1]\backslash \{\frac{1}{2}\}$.

Answer 2

Take any finite subset of the real line and remove any point(s), measure always remain the same(zero).

Answer 3

There exist nonempty sets of Lebesgue measure zero. Take such a set and one of its proper subsets.