The provided text discusses the concept of opposite statements and provides an example involving buildings and elevators. It defines opposite statements and asks for a continuation of the example. What is the definition of opposite statements as presented in the text? Analyze the first example provided, which involves buildings and elevators, and explain why the second statement is considered the opposite of the first, based on the provided logic.

Definition of Opposite Statements:

According to the text, two statements are considered opposite to each other if they cannot both be true and cannot both be false simultaneously. In simpler terms, if one statement is true, the other must be false, and vice versa.

Analysis of the Elevator Example:

The text presents two statements:

• Statement A: "В здании больше, чем 5 этажей" (The building has more than 5 floors).
• Statement B: "В этом здании должен быть лифт" (This building must have an elevator).

The first statement related to the rule is:

• Rule 1 (A → B): "Если в здании больше, чем 5 этажей, то в этом здании должен быть лифт." (If the building has more than 5 floors, then this building must have an elevator.)

The second statement, which is presented as the opposite, is:

• Rule 2 (¬A → ¬B): "Если в здании не больше, чем 5 этажей, то в этом здании не должно быть лифтов." (If the building does not have more than 5 floors [i.e., has 5 floors or less], then this building must not have an elevator.)

Explanation of Opposition:

These statements are considered opposites because:

• If Rule 1 is true (a building with more than 5 floors MUST have an elevator), then Rule 2 must also be true (a building with 5 floors or less MUST NOT have an elevator).
• Conversely, if Rule 1 is false (meaning a building with more than 5 floors does NOT necessarily have an elevator), then Rule 2 must also be false (meaning it IS permissible to have an elevator in a building with 5 floors or less).

The text explicitly states that statements A → B and ¬A → ¬B are called opposite to each other. This is because the negation of 'A → B' is 'A and ¬B', and the negation of '¬A → ¬B' is '¬A and B'. However, the text uses a simplified logical structure to illustrate the concept of opposite statements in this context, focusing on the direct implication and its contrapositive-like form where both the antecedent and consequent are negated. The core idea is that one statement asserts a condition and consequence, while the other asserts the absence of both the condition and the consequence.