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.

Answer with explanation:

Let two uncountable sets A and B .

(a).Let A= [2,3]=uncountable

B= [3,4)=uncountable

={3}= finite

Hence, is finite set .

(b).Let A= Set of positive real  numbers=Uncountable

B= Set of   negative real numbers and positive integers= Uncountable

Now, =Set of positive integer numbers  =countably infinite set.

Hence, is countably infinite .

(c). Let A= Set of real numbers=Uncountable

B= Set of irrational numbers  =Uncountable

Then, = Set of irrational numbers= Uncountable.

Hence, is uncountable when A is set of real numbers and B is set of irrational numbers.

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)