Let C be the set of points interior to or on the boundary of a cube with edge of length 1. Moreover, say that the cube is in the first octant with one vertex at the point (0, 0, 0) and an opposite vertex at the point (1, 1, 1). Let Q(C) ∫ ∫ ∫_C dxdydz.

(a) If C ⊂ C is the set {(x, y, z) : 0 < x < y < z < 1}, compute Q(C).

(b) If C is the subset {(x, y, z) : 0 < x = y = z < 1}, compute Q(C).