If, only if, if and only if

1. Sep 13, 2008

Trail_Builder

1. The problem statement, all variables and given/known data

Insert either "if", "only if", or "if and only if"..

x>2 ... x^2>9

2. Relevant equations

3. The attempt at a solution

I dont think any fit :S coonffuuuuuused

2. Sep 13, 2008

kehler

x can be any real number? In that case I *think* it should be "if".
But I'm no expert at this :P

3. Sep 13, 2008

dirk_mec1

if equals =>
only if equals <=
if and only if equals <=>

4. Sep 13, 2008

_Andreas

One fits perfectly. Think about what dirk said.

5. Sep 13, 2008

kehler

Oops sorry, guess I was wrong.

6. Sep 13, 2008

Trail_Builder

still dont know :S

I know the x^2>9 is equivalent to x<-3 or x>3.

so im guessing that rules out the <=>

and if it was the x>3, then I would stick the <= one in. ("only if").

"if" obviously wont work.

but dont you have to consider the x<-3 case too? or am I imposing somekind of weird necessary/sufficient crap in where i shouldn't?

7. Sep 13, 2008

_Andreas

Ponder the following. First, assume that x>2 is true. Does this imply that x^2>9 is true? If yes, then "if x>2, then x^2>9". If no, then not "if x>2, then x^2>9". (This is the "sufficient" condition.) Second, assume that x^2>9 is true. Does this imply that x>2 is true? If yes, then "only if x>2, then x^2>9". If no, then not "only if x>2, then x^2>9". (This is the "necessary" condition.) If yes to both, then "if and only if".

8. Sep 13, 2008

epenguin

Don't you also need to insert 'then' somewhere?

9. Sep 13, 2008

_Andreas

I think you need to know if there are any constraints on x. Can it be only a positive integer, perhaps? What does it say in your book?

10. Sep 14, 2008

Trail_Builder

thanks for the clarification. I kind just used my intuition before but glad to know how to properly do it, lol :).

the answer is no and no then, because there isnt a constaint on x... :S

so was I right in saying none?

11. Sep 14, 2008

Trail_Builder

no specified constaints

12. Sep 14, 2008

_Andreas

Yeah, if there are no constraints on x, then it seems to me that you were correct in that none fit. It is not necessary that x>2 for x^2>9. What's necessary is that x is not equal to 2. Neither is x>2 sufficient for x^2>9. (In other words I was wrong when I said one fits perfectly.)

Last edited: Sep 14, 2008