[!]. This exercise is used in Section e12.5. Suppose that El , E2 are Jordan regions in Rn.

(a) Prove that if El <:;;: E2, then Vol (Ed:::; Vol (E2)'

(b) Prove that El n E2 and El \ E2 are Jordan regions.

(c) Prove that if El , E2 are nonoverlapping, then Vol (El U E2) = Vol (Ed + Vol (E2)'

(d) If E2 <:;;: El , prove that Vol (El \ E2) = Vol (El ) - Vol (E2).

(e) Prove that Vol (El U E2) = Vol (El ) + Vol (E2) - Vol (El n E2)'