# NP-Hard problems which are not NP-Complete

1. Is it always true that a problem which is ${\sf NP}$-hard but not ${\sf NP}$-complete is an optimization problem such as Minimum-Vertex-Cover and many others.

2. Is it always true that a ${\sf NP}$-complete problem is always a decision problem such as vertex cover of size $k$, independent set of size $k$ and many others.