Question

Identify the hypothesis and the conclusion of each statement. School will be cancelled if it snows more than six inches.

Short answer

Hypothesis: it snows more than six inches; Conclusion: School will be cancelled.

Step-by-step solution

Identify the Conditional Statement Structure

A conditional statement is often expressed in an "if-then" form. In the given statement, "School will be cancelled if it snows more than six inches," the conditional statement structure can be observed where "it snows more than six inches" acts as the 'if' part, and "School will be cancelled" acts as the 'then' part.

Define the Hypothesis

In a conditional statement, the hypothesis is the part after 'if'. It presents the condition required for the conclusion to be true. In our example, the hypothesis is "it snows more than six inches." This is the condition that needs to occur to potentially trigger the conclusion.

Define the Conclusion

The conclusion in a conditional statement is the part that follows "then." It is the result or outcome that follows if the condition presented in the hypothesis is met. For the statement given, the conclusion is "School will be cancelled." This is what happens if the hypothesis is true.

Key concepts

Hypothesis and Conclusion

In the realm of geometry, statements often take the form of conditional expressions. Understanding the components of these statements is essential for effective logical reasoning.

Let's break down the parts. The **hypothesis** of a conditional statement is the part that follows the word "if." It represents the condition or premise that must be true for the statement to hold. For example, in the statement "School will be cancelled if it snows more than six inches," "it snows more than six inches" is the hypothesis. It sets the stage for the condition that must be met.

On the other hand, the **conclusion** is what follows the word "then," though it may not always be explicitly stated with "then." In our example, "School will be cancelled" constitutes the conclusion. The conclusion is the outcome that depends on the truth of the hypothesis. By clearly identifying the hypothesis and conclusion, students can better understand the logical flow within a statement and apply this understanding to various problems in geometry and beyond.

If-Then Statement

The **if-then statement** is a staple in both logical reasoning and geometry. It is a type of conditional statement that expresses a hypothesis followed by a conclusion, structured as "if something happens, then something else will occur." This logic is crucial in forming mathematical proofs and understanding relationships between different geometrical concepts.

These statements{