That the Ubaid period's distinctive style of painted pottery spread throughout Mesopotamia circa 5300 BC has been confirmed by carbon dating, but what is much more difficult to prove are the exact use to which the ancient Sumerians put the pottery.
a) has been confirmed by carbon dating, but what is much more difficult to prove
are Incorrect 'the exact use to which the ancient Sumerians put the pottery' - single subject matter, so is required - ......... prove is...
b)
have been confirmed by carbon dating, but what is much more difficult to prove
are IncorrectSV error - 'painted pottery' singular
c)
have been confirmed by carbon dating, but that which is much more difficult to prove is
IncorrectSV error - 'painted pottery' singular
d)
has been confirmed by carbon dating, but what is much more difficult to prove is Correcte)
are confirmed by carbon dating, but
that which is much more difficult to prove is
Incorrectthat which - wrong, meaning change