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Two planes do not intersect at all if the planes are parallel in three-dimensional space.

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Q: What would serve as a counter example to the statement Two planes intersect in exactly one line?
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What is a counterexample of All rectangles have two lines of symmetry?

Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.

An example that proves that a conjecture or statement is false?


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You figure it out!

Does every statement have a counter example?

Only some statements have both examples and counter examples. A sufficiently clear and unambiguous statement would not have counter examples.

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A counter example is a statement that shows conjecture is false.

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What is counter example?

A 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.

One way to show that a statement is NOT a good definition is to find a?

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All quadrilaterals with 4 right angles are squares. Which shape is a counter example to this statement?

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Is any two lines lie in exactly one plane?

Two lines can lie in one plane. For example, parallel lines are lines that intersect and lie in the same plane.

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).