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1. Hello there,
There is a question in a C3 paper that I did which asks me to 'prove, by counter-example, that the statement..... is false.'
Another type of question that was asked in another paper was to 'prove by contradiction'. How do I solve such problems, and could someone please provide me with some good links that I could refer to for a firm understanding of tackling such problems.
Thank you very much, in advance.
2. (Original post by Mini101)
Hello there,
There is a question in a C3 paper that I did which asks me to 'prove, by counter-example, that the statement..... is false.'
Another type of question that was asked in another paper was to 'prove by contradiction'. How do I solve such problems, and could someone please provide me with some good links that I could refer to for a firm understanding of tackling such problems.
Thank you very much, in advance.
Proof by counter-example simply requires you to give an example which shows that the statement isn't true (e.g. "All square numbers are even" is proven wrong by by 32).

Proof by contradiction requires you to show that, if the statement is true, you end up with an impossible result. There's a good example here.
3. (Original post by Plagioclase)
Proof by counter-example simply requires you to give an example which shows that the statement isn't true (e.g. "All square numbers are even" is proven wrong by by 32).

Proof by contradiction requires you to show that, if the statement is true, you end up with an impossible result. There's a good example here.
Thank you very much for the help. I understood what you said and I will also check the link you have provided.
Do you mind helping me with this question: prove by counter-example that {ln(3x^2+5x+3) is greater than or equal to 0 for all real values of x} is false.

Thank you once again.
4. (Original post by Mini101)
Thank you very much for the help. I understood what you said and I will also check the link you have provided.
Do you mind helping me with this question: prove by counter-example that {ln(3x^2+5x+3) is greater than or equal to 0 for all real values of x} is false.

Thank you once again.
Let x = -0.75
f(x) = -0.06, which is not greater than or equal to 0, hence the statement is wrong.

If you're wondering how I came up with that, remember that ln(x)<0 if x<1, so if 3x^2+5x+3 is <1 for any real value of x, ln(3x^2+5x+3) will be <0.
5. (Original post by Plagioclase)
Let x = -0.75
f(x) = -0.06, which is not greater than or equal to 0, hence the statement is wrong.

If you're wondering how I came up with that, remember that ln(x)< x<1, so if 3x^2+5x+3 is <1 for any real value of x, ln(3x^2+5x+3) will be <0.
OHHHH! Wow! I get it now....
Thank you very very much!

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