Question

If A and B are both uncountably infinite sets then A - B could be? Select...

If A and B are both uncountably infinite sets then A - B could be? Select one of the following options:
a) Uncountably infinite
b) Finite
c) Countably infinite

Explain the solution.

Math   Advanced-Math   
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Homework Answers

Answer #1

Any doubt then comment below...

I think you forget to write one option...

Because , here all cases are possible...

Example...

If we take A=(0,2) and B=(0,1) then A-B = [1,2) ...

Here A and B are uncountable infinite then their difference is also uncountablly infinite....

Now if we take A=(0,1] , B=(0,1) ...then A-B = {1} .. here difference is finite set ...

If we take A= (0,1)UN ... Here U represent union and N represent natural number..

And B =(0,1) ...then A-B =N ...this is countably finite...

So we see that all cases are possible for different choices of A and B ...

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