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Question: Define counter example. give an example

Posted by: Shrigesh on 29.10.2020

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A counter is an instance where a  rule/theorem/law, which is generally valid otherwise in most of the cases, is not valid in the particular case. Counter of any rule is an example of an instance, where the rule is not applicable or an exception. to the rule.To illustrate ,let us consider the rule for finding Leap Year. 

We know that there are 366 days in a leap year, that is the month of February has 29 days in a leap year. The general rule is, if the year is divisible by 4,then it is a leap year. That is if the numerical value of any year is a multiple of 4,then the year is a leap year.Thus,1980,1992,2012 ,2020 etc. are leap years. But this rule is not valid ,if the year is a century year, that is the last 2 digits of the year are 0,0.Thus the century years 1800,1900,2100,2200,2300  etc. are not leap years ,though they are multiples of 4. These are counter examples for the general rule of leap year.

Again this rule is not valid if the  century years are multiples of 400 ,because century years which are multiples of 400 are leap years .Thus century years 1600,2000,2400 etc. are century leap years having 366 days. These  are again counter examples for the general rule of  leap years for century years.   

Answer:
An example that proves that statement is either true or false..such an example is called counterexample because it's an example that counters,or goes against ,the statement's conclusion.For example,the prime number 2 is a counterexample to the statement"All prime number are odd".
Answer:
If you are able to give an example to prove the given statement as wrong is called a counter example. For example, "All prime numbers are odd numbers" is the given statement. We know that 2 is a prime number, but it an even number. Therefor the given statement is wrong. This is a counter example of the given statement.
Answer:
If you are able give an example to prove the given statement as wrong, then the example is called counter example. For example, "All prime numbers are odd" is the given statement. But 2 is a prime number and 2 is not an even number. Therefore the given statement is wrong. This is a counter example for the given statement.
Answer:
The example who can prove the statement wrong or false. This type of example called counter example. Example:-every icecream is chocolatey but butterscotch is also a icecream. Here butterscotch icecream is the counter example of the statement.

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