micromass said:Yes, (a) is correct!
xlalcciax said:Thanks!
Can You give me some clues for b) ?
nicksauce said:Think of a periodic function that is odd or even. Now phase shift it slightly. Is it still odd or even?
Any odd function which is continuous on (−∞, +∞), passes through the origin.xlalcciax said:Thanks!
Can You give me some clues for b) ?
A counter example is a specific example or instance that disproves a general statement or mapping. In other words, it is a situation or scenario that goes against the proposed mapping, thus showing that the mapping is not always true.
Counter examples are used to show that a proposed mapping is not always true by providing a specific instance where the mapping does not hold. This proves that the mapping is not universally valid and therefore cannot be considered as a valid rule or statement.
Yes, a single counter example can be enough to disprove a mapping. This is because the mapping is meant to hold true for all possible scenarios, and a single instance where it does not hold is enough to show that it is not a universally true statement.
No, counter examples can be used in various fields and contexts, not just in mathematics. They can be used to disprove hypotheses, theories, and general statements in any field of study, as long as there is a clear mapping or relationship being proposed.
No, counter examples are only used to disprove mappings. If a counter example is found, then the mapping is considered invalid. However, multiple examples that support a mapping can be used to provide evidence for its validity, but they cannot prove it definitively.