Countable and uncountable Self Doubt 1

Question

which of the following is always correct?
A. Union of two uncountable set is uncountable
B. The intersection of two uncountable set is uncountable
C. Union of two uncountable set is countable
D. The intersection of two uncountable set is countable
E. Union of an uncountable and countable set is uncountable
F. The intersection of an uncountable and countable set is uncountable
G. Union of a countable and countable set is countable
H. The intersection of a countable and countable set is countable
I. The complement of a countable set is countable.
J. The complement of a countable set is uncountable.

Comments

A. TRUE 
(Uncountable) U (Uncountable) = Uncountable
B. May or may not be TRUE
Can be TRUE when both the sets are same. 
Can be FALSE when both the sets are having finite number of elements in common
C. FALSE
(Uncountable) U (Uncountable) = Uncountable
D. May or may not be TRUE
Can be TRUE when both the sets are same. 
Can be FALSE when both the sets are having finite number of elements in common
E. TRUE
(Uncountable) U (Countable) = Uncountable
F. False
(Uncountable) INTERSECTION (Countable) = Countable
G. TRUE
(Countable) U (Countable) = Countable
H. TRUE
(Countable) INTERSECTION (Countable) = Countable
I. May or may not be TRUE
Complement of a Countable set can be anything:

1. Finite. Consider S={1,2} S belongs to Z and 1<=S<=3.Then complement of S = {3}
2. Countable. Consider S=set of all odd positive integers, Then complement of S=set of all even positive integers
3. Uncountable. S={1} S belongs to the set of R. Then Complement of S = All Real Numbers except 1.

J. May or may not be TRUE
Same argument as above.

 

(Uncountable) U (Uncountable) = Uncountable
(Countable) U (Countable) = Countable
(Uncountable) U (Countable) = Uncountable
(Uncountable) Intersection (Countable) = Countable
(Countable) Intersection (Countable) = Countable
(Uncountable) Intersection (Uncountable) = Countable/Uncountable
Complement(Countable) = Countable/Uncountable
Complement(Uncountable) = Countable/Uncountable