"If and only if" (1 Viewer)

[Estel]

Just a quick question as to what you actually have to prove if the question says (for eg)... prove x^2=y if and only if yadaa...

 

[CrashOveride]

prove it under some conditions??

whats the actual question

 

[Xayma]

You have to prove that it ONLY occurs under that condition.

I think it means that the converse will be true.

 

[Estel]

How do u prove it ONLY occurs under that condition? Confusing...

 

[CrashOveride]

Estel: Post up the bloody question =p

 

[Estel]

It's rather useless without the accompanying material... and I don't really want to be accused of cheating (it's for mathsearch). I just want to know a general answer for how to answer an 'if and only if' question.

 

[kimmeh]

Originally posted by CrashOveride
prove it under some conditions??

thats what i interpret it as, iff, only under certain conditions

 

[martin]

If and only if means that you need to prove it both ways.

Casting around desperately for an example I find my analysis lecture notes

"A monotone sequence converges if and only if it is bounded"

Now without worrying about what the words mean this means that:

if a monotone sequence is bounded it converges

AND

if a monotone sequence converges it is bounded

So to prove that x^2 = y iff something you need to prove that something implies x^2 = y and that x^2 = y implies something.

cheers,
Martin

 

[kpq_sniper017]

Originally posted by Estel
It's rather useless without the accompanying material... and I don't really want to be accused of cheating (it's for mathsearch). I just want to know a general answer for how to answer an 'if and only if' question.

either way, asking for help is still cheating
well, i guess it's not "cheating in a sense", but then again, what's the point of getting a prize/certificate if u didn't do it according to the suggested rules.

just on that.....i handed mine in today: only did around 10 exercises - estel, did u do every exercise up to Ex 22??? coz i just didn't bother.....lol - had more important things to do. ah well.

 

[Xayma]

Originally posted by martin
Now without worrying about what the words mean this means that:

if a monotone sequence is bounded it converges

AND

if a monotone sequence converges it is bounded

So basically you just prove that the first statement and its converse are true?

 

[Estel]

I didn't get a chance to read martin's comment before handing it in this morning... ahh well... least I can say I obtained zero help for the entire project...
I attempted every question seriously- up to 26. Tho I didn't prove the converses for the 'if and only if' theorems, and hence I shall lose valuable marks there for 2 questions.

*Wants to go to NMSS*
*Doubts will make it*

There are probably better things to do but the Abstract Cubolinear System was pretty neat you have to admit ...

 

[martin]

So basically you just prove that the first statement and its converse are true?

Yep

 

[Affinity]

I like to think of it as a road..
if is one ay traffic
and if and only if is two way.

 

[Estel]

All very helpful advice... just two days late

 

[KeypadSDM]

Best way to prove it.

Prove both of these:

A => B
and
~A => ~B

I love that method, so cool.

 

[Xayma]

Whats the ~A mean?

 

[velox]

Read the cambridge book, i think it explains in there

 

[KeypadSDM]

If you need to show that y = x^2 proves something, sub in y = x^2, show the answer comes out, then sub in y = x^2 + c, and show the answer doesn't come out unless c = 0

The ~ means "not"

So prove that A implies B and that not A implies not B

 

[Estel]

ooh thanks for that keypad... another technique to use.