Are all parallelograms quadrilaterals

Yes! Every parallelogram is a quadrilateral.

Explanation

Every parallelogram is a quadrilateral. But vice versa is not true ie every quadrilateral is not a parallelogram. Quadrilateral is a 4 sided polygon & parallelogram is also a 4 sided polygon but with some extra characteristics. That is the reason, every parallelogram is a quadrilateral. But if quadrilateral gets all those extra characteristics, then only it becomes a parallelogram.