Let $(X, d)$ be a metric space and let $A$ and $B$ be subsets of $X$. Define $d(A,B) = \inf\{d(a, b) : a \in A, b\in B\}$. Pick out the true statements.
a. If $A$ and $B$ are disjoint, then $d(A,B) > 0$.
b. If $A$ and $B$ are closed and disjoint, then $d(A,B) > 0$.
c. If $A$ and $B$ are compact and disjoint, then $d(A,B) > 0$.
My answer is- a is not true if $A$ & $B$ are open and they have a common limit point . b & c are true. Am I correct?