DirectX 9-capable video hardware. Aspire S5-371-52JR?

Thank you, IronFly. But is video hardware that is DirectX 12-capable also DirectX 9-capable? (More generally, is hardware that is DirectX n-capable also DirectX m-capable, where m < n?) I suppose that for that to be true, DirectX 12 would have to be a superset of DirectX 9; hardware that supports the superset must support the subset. Also, since DirectX is not one but a collection of APIs, for each API in DirectX 9, the corresponding API in DirectX 12 would have to be not only present, but itself a superset of the same API in DirectX 9.