Let A be any uncountable set, for instance [0, 1] or R. (a) Remove a finite number of values from A to make B. (b) Remove a countably finite number of values from A to make B. (c) Use either of the sets removed in parts (a) and (b) to make B. For instance if B = A - {0.5}, then B is uncountable and A - B is {0.5}. And if B is {0.5} then A - B is uncountable.
Answers & Comments
Verified answer
A-B is finite:
A=all real numbers >=0, B=all real numbers >0
A-B is countably finite:
A=all real numbers, B= all real numbers except the integers
A-B is uncountable:
A=all real numbers, B=all positive real numbers
Uncountable Sets
Let A be any uncountable set, for instance [0, 1] or R. (a) Remove a finite number of values from A to make B. (b) Remove a countably finite number of values from A to make B. (c) Use either of the sets removed in parts (a) and (b) to make B. For instance if B = A - {0.5}, then B is uncountable and A - B is {0.5}. And if B is {0.5} then A - B is uncountable.