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A counter example occurs when somebody makes a claim that all members of some category of things have a particular property, and then someone else proves that the claim is not true by showing an example of a thing in the category that does not have the property claimed.
For example, if someone claimed that "All presidents of the United States are dead white men", then Barack Obama would be a counter-example because he is a President of the United States but isn't a dead white man.
For another example, if someone claimed that all mammals bear live young, the echidna and the platypus would be counter-examples because they are mammals that lay eggs.
For another example, if someone claimed that the United States is the only country that has never defaulted on its debts, Australia and Tuvalu would be counter-examples. The claim is logically equivalent to saying that all countries in the category of being not the USA have defaulted on a debt at least once,....
For another example, if someone claimed that all prime numbers are odd, "2" would be a counter example. Or if someone claimed that all odd numbers are prime "9" would be a counter-example.
In short, a counter-example to a proposition or claim is an example that proves that the proposition or claim is not true.
Wiki User
∙ 11y ago
Wiki User
∙ 14y agoA counter example is a proof of a negation of a universal statement.
A statement of the form "all X are Y" (e.g. all men are mortal), can be disproved by providing a counter example (here: something (someone) which is both a man and immortal).
A more mathematical example of the use of a counter example could be to disprove the statement "the product of two prime numbers is odd". This is a claim about all numbers which are the product of two prime numbers (all elements in the set {n in N | n = p*q where p and q are prime numbers}). This set contains infinitely many pair numbers, but a single example (or witness), is enough to disprove the statement. Four is such a number and can serve as a counter example.
Wiki User
∙ 15y agoAn example that proves a conjecture to be false.
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Is it really possible to avoid reactive power in electrical circuit?
yesAnswerNo, but you can counter its effects. For example, if your load is inductive, then you can counter the effects of its inductive reactance by introducing capacitors with equal capacitive reactance.
What are some slogans for over the counter drugs?
Don't buy over the counter drugs... Buy over the counter PUGS! (DOGS)
What is the difference in booking a ticket from railway counter to that in irctc?
I saves time queuing up at the counter. Saves money on travel from house to booking counter.
What are the release dates for Behind the Counter - 1928?
Behind the Counter - 1928 was released on: USA: 3 March 1928
Is over the counter is a collective noun?
No, the term 'over the counter' is not a noun at all.The term 'over the counter' is a compound adjective, a word used to describe a noun.The adjective 'over the counter' is used to describe medicine that can be purchased without a prescription or stocks not transacted through an organized securities exchange.
How do you use counter example in a sentence?
your face is a counter
An example which proves a conjecture false?
Counter Example
What is an example that shows conjecture is not true?
A counter-example.
What is a counter example of why integers aren't closed under division?
An example would be 2 ÷ 4 = 0.5 A counter example would be 4 ÷ 2 = 2
An example that proves that a conjecture or statement is false?
Counter-example
An example used to show that a given statement is not always true?
counter example
How can you use the word counter in a sentence?
It can be used in a number of ways. For example, "The legislator's plan ran counter to what his party was trying to accomplish as a whole." Counter in this sentence means against, literally in opposition to. Here's another example, "They set the groceries on the counter." Counter used here refers to the flat surface in most kitchens.
What is the if-then form of A counter example invalidates a statement?
You figure it out!
How can you prove that a conjecture is false?
Give a counter-example.
Turning a while loop to a for loop?
A for loop is just a while loop with a built-in counter. For example, the following programs are functionally identical: While loop: int counter = 0; while(counter < 10) { printf("counter = %d\n", counter); counter++; } For loop: for(int counter = 0; counter < 10; counter++) { printf("counter = %d\n", counter); }
What is spawn's counter?
The counter represents the amount of magic power he is using up. The counter starts at 9:9:9:9 and every time for example, gets into a fight, the counter drops.
What does counter example mean in math terms?
It is an example that demonstrates, by its very existence, that an assertion is false. Usually experience suggests that the assertion is true: there is a large amount of supporting "evidence" but the statement has not been proven. The counter-example, though demolishes the assertion For example: Assertion: all prime numbers are odd. Counter example: 2. It is a prime but it is not odd. Therefore the assertion is false. This was a favourite "trap" at GCSE exams in the UK. Assertion: if you divide a nuber it becomes smaller. Counter example 1: 2 divided by a half is, in fact, 4. Counter example 2: -10 divided by 2 is -5 (which is larger by being less negative).
