What is a counterexample of a false proposition?

A counterexample of a false proposition is an example that does not meet the conditions and results of this proposition.

For example, the proposition "Any even number is a multiple of 8" proves that the proposition "Any even number is a multiple of 8" is a counterexample of a false proposition. You must meet the condition that it is an even number instead of a multiple of 8, and you can choose numbers such as 2, 4 and 6.

A true proposition means that if the proposition is established, then the conclusion must also be established. A proposition can be written in this format: if+conditions, then+conclusions. The proposition with contradictory conditions and results is a false proposition.

Extended data

False propositions can be divided into three categories:

1, the topic only corresponds to one background, and the conclusion is wrong. For example, "1+2=5" is a false proposition.

The topic corresponds to various backgrounds, and the conclusion is wrong for them. For example, "Two straight lines are parallel and the internal angles on the same side are complementary", and the title of this proposition corresponds to various backgrounds: for all backgrounds, the internal angles on the same side are complementary rather than complementary. This proposition is a false proposition.

3. The topic corresponds to a variety of backgrounds, and the conclusion is wrong for some people and correct for others.

For example, the proposition that "two straight lines are parallel and the internal angles on the same side are equal" corresponds to various backgrounds: for a bunch of backgrounds, one angle of the internal angles on the same side is greater than 90, the other angle is less than 90, and the internal angles on the same side are not equal; But for another background, both angles of the same side internal angle are equal to 90, and the same side internal angle is equal.

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