Answer with explanation:
Let two uncountable sets A and B .
(a).Let A= [2,3]=uncountable
B= [3,4)=uncountable
[tex]A\cap B [/tex]={3}= finite
Hence, [tex] A\cap B [/tex] is finite set .
(b).Let A= Set of positive real numbers=Uncountable
B= Set of negative real numbers and positive integers= Uncountable
Now, [tex]A\cap B[/tex]=Set of positive integer numbers =countably infinite set.
Hence, [tex]A\cap B[/tex]is countably infinite .
(c). Let A= Set of real numbers=Uncountable
B= Set of irrational numbers =Uncountable
Then, [tex]A\cap B[/tex]= Set of irrational numbers= Uncountable.
Hence, [tex]A\cap B[/tex] is uncountable when A is set of real numbers and B is set of irrational numbers.
