Question

Можно ли, доказав прямую теорему ,принять обратную к ней без доказательства? Пожалуйста!!!!!​

Answer 1

Ответ:

Нет. Прямая теорема: любое число, кратное 10 - чётное. Верная.

Однако не любое чётное число делится на 10.

Объяснение:

Answer 2

Can you accept the inverse of a direct theorem without proof?

When it comes to mathematical theorems, it is generally not possible to accept the inverse of a direct theorem without proof. The reason for this is that the inverse of a theorem may not necessarily be true, even if the original theorem is proven to be true. In mathematics, the inverse of a statement is formed by negating both the hypothesis and the conclusion of the original statement.

To illustrate this, let's consider a hypothetical direct theorem and its inverse:

Direct Theorem: If a number is divisible by 2, then it is even.

Inverse Theorem: If a number is not divisible by 2, then it is not even.

In this case, the direct theorem has been proven to be true, but the inverse theorem is not necessarily true. There are numbers that are not divisible by 2 but are still even (e.g., 0), which means the inverse theorem is false.

Therefore, to accept the inverse of a direct theorem, it is necessary to provide a separate proof for the inverse statement. Simply proving the direct theorem does not automatically validate its inverse.