# Thread: A simple logic problem

1. ## A simple logic problem

Hi,

If X^2 >= 100 then it follows that X >= 10 or X<= 0. Is this statement true?

I'm aware that it would certainly be true if the second part was X>= 10 or X<= -10. But I suppose as X<= 0 is more general that X<= -10 (X<=-10 is a subset of X<=0) then it holds as being correct.

I am right in thinking this?

Sorry if this is in the incorrect sub forum...

Thanks!

2. Originally Posted by Ant
Hi,

If X^2 >= 100 then it follows that X >= 10 or X<= 0. Is this statement true?

I'm aware that it would certainly be true if the second part was X>= 10 or X<= -10. But I suppose as X<= 0 is more general that X<= -10 (X<=-10 is a subset of X<=0) then it holds as being correct.

I am right in thinking this?

Sorry if this is in the incorrect sub forum...

Thanks!

Precisely because it is more general it isn't true: take $x=-1<0$ . This number fulfills your condition, but $x^2=1\ngeq 10$ ...

Tonio

3. Thanks for your response, I can quite see that your counter example works well. But it's still giving me some trouble.

If the statement was reduced further to:

X^2 >= 100 then it follows that X>= 0 or X<= 0.

Can't the above statement be summarized by saying 'if X squared is greater or equal to 100 then the X is either a positive number of a negative number or it is zero. This is true is it not?

4. Originally Posted by Ant
Thanks for your response, I can quite see that your counter example works well. But it's still giving me some trouble.

If the statement was reduced further to:

X^2 >= 100 then it follows that X>= 0 or X<= 0.

Can't the above statement be summarized by saying 'if X squared is greater or equal to 100 then the X is either a positive number of a negative number or it is zero. This is true is it not?

I think I'm beginning to get your logic, and thus I should also change my previous answer: yes, it is true.

Of course, it is understood that we're talking of real numbers here...

The other way around, though, is not true.

Tonio

5. Of course, it is understood that we're talking of real numbers here...
Is OP question can be asked when x in C(complex)? (hmmm...)

6. Originally Posted by tonio
I think I'm beginning to get your logic, and thus I should also change my previous answer: yes, it is true.

Of course, it is understood that we're talking of real numbers here...

The other way around, though, is not true.

Tonio
Yes, sorry, I probably should have stated that. It is given that X is an element of the set of real numbers.