3. [6 Pts] Give an example of two uncountable sets A and B such that AnB is (a) finite, (b) countably infinite, (c) uncountably infinite.
Accepted Solution
A:
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=UncountableB= Set of negative real numbers and positive integers= UncountableNow, [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=UncountableB= Set of irrational numbers =UncountableThen, [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.