\ 8. Under the sseumptions of Problem 7, prove that

f

is one-one if and oaly if the sign

sup

in (e) can be replaced by

=

for all

Asubx

, and

f

is onto if and oaly if the sign

C

in (f) can be replaced by = for all

CsubY

.

8. Under the asoumptions of Problem 7, prove that f is one-one if and oaly if the sign in (e) can be replaced by = for all AX, and f is onto if and oaly if the sign C in (f) can be replaced by = for all CY