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What is an example that shows conjecture is not true?
A 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.
How can you prove that a conjecture is false?
Give a counter-example.
What is the if-then form of A counter example invalidates a statement?
You figure it out!
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).
