Suppose that E1, E2 are Jordan regions in Rn. a) Prove that if E1 E2, then b)

Suppose that E1, E2 are Jordan regions in Rn.
a) Prove that if E1 Š‚ E2, then

b) Prove that E1 ˆ© E2 and E1 E2 are Jordan regions.
c) Prove that if E1, E2 are nonoverlapping, then
Vol(E1 ‹ƒ E2) = Vol(E1) + Vol(E2).
d) If E2 Š‚ E1, prove that
Vol(E1 E2) = Vol(E1) - Vol(E2).
e) Prove that
Vol(E1 U E2) = Vol(E1) + Vol(E2) - Vol(E1 ˆ© E2).

Transcribed Image Text:

Vol(E) S Vol (E2)