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:
- Finite. Consider S={1,2} S belongs to Z and 1<=S<=3.Then complement of S = {3}
- Countable. Consider S=set of all odd positive integers, Then complement of S=set of all even positive integers
- 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