Questions and Answers

- 1.
### A statement that requires proof.

Explanation

A postulate is a statement that is accepted as true without proof, and therefore it does not require proof. It is an assumption or a starting point for further reasoning or deduction. In this context, a statement that requires proof would be the opposite of a postulate, as it would need evidence or logical reasoning to support its validity.Rate this question:

- 2.
### The first part of an if-then statement.

Explanation

The given correct answer is "hypothesis". In an if-then statement, also known as a conditional statement, the first part is called the hypothesis. It is the statement that follows the "if" and presents a condition or situation that needs to be fulfilled. The hypothesis sets the condition for the second part of the statement, which is the conclusion or result that follows the "then".Rate this question:

- 3.
### Uses the laws of mathematics to reach logical conclusions from given statements.

Explanation

Deductive reasoning is a process that utilizes the laws of mathematics to draw logical conclusions from given statements. It involves starting with general principles or premises and then applying logical rules to reach specific conclusions. In deductive reasoning, the conclusions are guaranteed to be true if the initial premises are true. This method is commonly used in mathematics, logic, and problem-solving to derive accurate and reliable results.Rate this question:

- 4.
### Is formed by negating the hypothsis and conclusion of a conditional.

Explanation

The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion of the original statement. In other words, if the original statement is "If A, then B," then its inverse would be "If not A, then not B." This is a valid logical operation that allows us to explore the relationship between the hypothesis and conclusion of a conditional statement from a different perspective.Rate this question:

- 5.
### Is formed by joining two or more statements with the word and

Explanation

A conjunction is a word that is used to join two or more statements together. It helps to combine these statements and show the relationship between them. In this case, the correct answer is "conjunction" because it accurately describes the function of joining two or more statements with the word "and".Rate this question:

- 6.
### A statement that is accepted as true without proof.

- 7.
### Is formed by exchanging the hypothesis and conclusion of a conditional.

Explanation

The converse of a conditional statement is formed by exchanging the hypothesis and conclusion of the original statement. In other words, if we have a statement "If A, then B", the converse would be "If B, then A". This is a valid logical operation, as it explores the relationship between the hypothesis and conclusion from a different perspective. It is important to note that the converse may or may not be true, as it does not necessarily preserve the truth value of the original statement.Rate this question:

- 8.
### To show that a conjecture is false, you would provide ______.

Explanation

A counterexample is a specific example or case that contradicts a conjecture or hypothesis. It is used to demonstrate that the conjecture is false by providing a single instance where it fails to hold true. By presenting a counterexample, it shows that the conjecture does not hold universally and can be disproven.Rate this question:

- 9.
### A statement p would be written in the form, not p.

Explanation

The given correct answer is "inverse." In logic, the inverse of a statement is formed by negating the original statement. In this case, the original statement is "p," and the inverse would be "not p." The inverse of a statement is a way to express the opposite meaning of the original statement.Rate this question:

- 10.
### In a two-column proof, the properties that justify each step are called ______.

Explanation

In a two-column proof, the properties that justify each step are called reasons. These reasons provide logical explanations or justifications for why a particular step or statement is true or valid. They help demonstrate the logical flow and validity of the proof, ensuring that each step is supported by a valid property or theorem.Rate this question:

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