Question

Give an example of two uncountable sets A and B such that A - B is:

a) Finite
b) Countably infinite
c) Uncountable
d) None of the above

Answer 1

An example of two uncountable sets A and B such that A - B is: finite, countably infinite, uncountable, or none of the above.

Step-by-step explanation:

An example of two uncountable sets A and B such that A - B is:

1. a) Finite: Let A = [1,2,3,4,5] and B = [3,4,5]. Here, A - B = [1,2] which is a finite set.
2. b) Countably infinite: Let A = [1,2,3,4,5,...] and B = [3,4,5,...]. Here, A - B = [1,2] which is a finite set.
3. c) Uncountable: Let A be the set of all real numbers and B be the set of all integers. Here, A - B = the set of all non-integer real numbers which is uncountable.
4. d) None of the above: There can be various examples where A - B does not fall into any of the above categories.