a)

Generally, the plane is determined by the coordinated axis is the xy-plane, whose standard equation by \(\displaystyle{z}={0}\).

From equation \(\displaystyle{y}\ge{x}^{2},{z}\ge{0},{y}={x}^{2}\) represent the parabola curve in the xy-plane and all point above the region \(\displaystyle{z}={0}.\)

Figure 1 shows for \(\displaystyle{y}\ge{x}^{2},{z}\ge{0}\) in the Cartesian coordinate system.

Thuse, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for \(\displaystyle{y}\ge{x}^{2},{z}\ge{0}\) is the region inside the parabola \(\displaystyle{y}\ge{x}^{2}\) in the xy-plane.

b)

From equation \(\displaystyle{x}\le{y}^{2},{0}\le{z}\le{2},{x}={y}^{2}\) represent the parabola curve in the xy-plane in the region on or to the left of the parabola and also have all point above the region from \(\displaystyle{z}={0}\to{z}={2}.\)

Figure 2 shows for \(\displaystyle{x}\le{y}^{2},{0}\le{z}\le{2}\) in the Cartesian coordinate system.

Thus, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for \(\displaystyle{x}\le{y}^{2},{0}\le{x}\le{2}\) is the region on or to the left the parabola \(\displaystyle{x}\le{y}^{2}\) in the xy-plane and all points from \(\displaystyle{z}={0}\to{z}={2}.\)