Problem Solving

jainpiyushjain wrote:Q. If A² -B² > 0

Answer true or false

Is A>B and A<-B ?

(A² - B²) = (A - B)(A + B) > 0

Hence, either

• (A - B) > 0 and (A + B) > 0 ---> A > B and A > -B
  
  OR
  
  (A - B) < 0 and (A + B) < 0 ---> A < B and A < -B

Hence, it is not possible that both of them together is true.
Hence, the statement is FALSE (if answering in true/false) or NO (if answering in yes/no).

EDIT:
in my original post, i read the inequality signs backward (ah, the joy of being dyslexic).

i've deleted the discussion of things that the problem didn't actually say.
(:

Anju@Gurome wrote:So without any other information it is impossible to answer your question as in either case the answer will be YES for one half and NO for the other half.

--> this actually answers the question, then. i.e., anything of the form "true statement AND false statement" is false. so, you've actually proved that the answer is "no", not "we can't tell".

the problem here is, of course, the initial confusion created by the strange problem statement.

lunarpower wrote:

Anju@Gurome wrote:So without any other information it is impossible to answer your question as in either case the answer will be YES for one half and NO for the other half.

--> this actually answers the question, then. i.e., anything of the form "true statement AND false statement" is false. so, you've actually proved that the answer is "no", not "we can't tell".

I agree with you but then again he asked to answer in "true or false".

lunarpower wrote:my first comment here is that you'll never see anything that looks like this:

jainpiyushjain wrote:Is A>B and A<-B ?

if you have simultaneous inequalities that both involve the same quantity -- here, "A" -- then they should be combined. so, this question should be written as follows:
"Is -b < a < b?"

It should be other way around, i.e. B < A < -B

If you are suggesting a modification of the question or what the question should've been then ignore this part of the post.

Anju@Gurome wrote: I think what he has asked cannot be combined to any simple inequality as both of them together never going to hold true.

If you are suggesting a modification of the question or what the question should've been then ignore this part of the post.

ah, i read the inequality signs backwards. thanks.
i will edit my post.

on the other hand, my other observation still holds: if you have "statement 1 AND statement 2", and you know that exactly one of statements 1 and 2 is true while the other is false, then "statement 1 AND statement 2" is false. it's not indeterminate -- "yes AND no" = no.

"true AND false" is false.

lunarpower wrote:on the other hand, my other observation still holds: if you have "statement 1 AND statement 2", and you know that exactly one of statements 1 and 2 is true while the other is false, then "statement 1 AND statement 2" is false. it's not indeterminate -- "yes AND no" = no.

"true AND false" is false.

Yes, I agree.
Let me edit my reply too.