Countable and Uncountable Self Doubt 2

Question

Which of the following is always correct?
A. Cross product of two countable set is countable
B. Cross product of two countable set is uncountable
C. Cross product of two uncountable set is countable
D. Cross product of uncountable and countable set is uncountable
E. Cross product of uncountable and countable set is countable
F. Cross product of uncountable and countable set is uncountable

Comments

(Uncountable) X (Uncountable) = Uncountable
(Countable) X (Countable) = Countable
(Uncountable) X (Countable) = Uncountable

Cartesian product of finitely many Countable sets is Countable. However Cartesian product of Infinitely many Countable sets is Uncountable.

Answer 1

If countable × countable then answer countable .

uncountable ×uncountable then ans uncountable