I need counter example for these statement

In summary, a counter example is a specific instance that disproves a statement or theory. It is important to find counter examples to identify flaws in our understanding and improve our conclusions. To find a counter example, one can assume the statement is true and look for exceptions or use logical reasoning. A counter example can completely disprove a statement, and they can be used in various fields, not just in scientific research.
  • #1
haya
15
0

Homework Statement


[PLAIN]http://hh7.net/Apr1/hh7.net_13016941501.gif


Homework Equations



these statement are false and i need counter example for each one

The Attempt at a Solution



for(ii) i can say that f(x)=x2-4 on [-6,6]

for others i need help
 
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  • #2
For (iii), what about f(x) = 0?

[edit]For (iv), what about g(x) = x + 1?[/edit]
 

1. Can you explain what a counter example is?

A counter example is a specific instance or case that disproves a statement or theory. It demonstrates that the statement is not always true and can be false under certain conditions.

2. Why is it important to find counter examples?

Finding counter examples can help us identify flaws or limitations in our understanding of a concept or theory. It allows us to refine our ideas and make more accurate conclusions.

3. How do you go about finding a counter example?

To find a counter example, you can start by assuming the statement is true and then looking for potential exceptions or situations where the statement may not hold. It may also involve testing different scenarios or using logical reasoning to identify contradictions.

4. Can a counter example completely disprove a statement?

Yes, a counter example can completely disprove a statement. If a counter example is found, it means the statement is not always true and therefore cannot be considered a valid or universal truth.

5. Are counter examples only used in scientific research?

No, counter examples can be used in any field where theories or statements are being tested and evaluated. They can be used in mathematics, philosophy, and everyday life situations as well.

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