This may seem like a trivial question (and I think I know the answer, just wanna check if it´s correct).
We have a function $f:\Bbb R^n \rightarrow\Bbb R$ and subsests $Y \subseteq X \subseteq\Bbb R^n$ and a point $x \in Y.$ Two verdicts:
a) $f$ has its minimum in $x$ on subset $X$
b) $f$ has its minimum in $x$ on subset $Y$
Does one verdict imply the other? I think that a implies b because $\forall x \in X: x \in Y$ and therefor there couldnt exist $y \in Y = \min(f): y \notin X$. Is this correct? Are there some other implications? Thanks