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# Algebraic Proofs Flashcards

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@EasygoingAgate6318

### What is the definition of 'given'?

• A process of reasoning
• An example
• A conclusion
• A hypothesis (correct)
• ### What does 'prove' mean?

• A statement following IF
• A negation
• A process of reasoning
• A conclusion (correct)
• ### What is the Reflexive Property?

If A, then A=A

### Explain the Symmetric Property.

<p>If A=B, then B=A</p> Signup and view all the answers

### What does the Distributive Property state?

<p>If A(B+C), then AB+AC</p> Signup and view all the answers

### Describe the Substitution Property.

<p>If A=X, then X can be substituted for A</p> Signup and view all the answers

### What is the Transitive Property?

<p>If A=B, and B=C, then A=C</p> Signup and view all the answers

<p>If A=B, then A+X=B+X</p> Signup and view all the answers

### What is the Multiplication Property?

<p>If A=B, then A×B=B×A</p> Signup and view all the answers

### Describe the Division Property.

<p>If A=B, then A/X=B/X</p> Signup and view all the answers

### What is a conjecture?

<p>A statement that gives an example that follows the hypothesis, but not the conclusion</p> Signup and view all the answers

### Define inductive reasoning.

<p>A process that includes looking for patterns and making conjectures, which are unproven statements based on observations</p> Signup and view all the answers

### What are conditional statements?

<p>If-Then statements</p> Signup and view all the answers

### Explain what a converse is.

<p>Interchanging the hypothesis and the conclusion of a conditional statement</p> Signup and view all the answers

### What is an inverse in logic?

<p>Formed by negating both the hypothesis and conclusion</p> Signup and view all the answers

### Define contrapositive.

<p>Formed by negating both the hypothesis and conclusion of the converse of a statement</p> Signup and view all the answers

### Provide an example of If-Then form.

<p>If it is snowing, then it is cold</p> Signup and view all the answers

### What is a hypothesis?

<p>A phrase following, but not including IF</p> Signup and view all the answers

### Define conclusion.

<p>The phrase following but not including THEN</p> Signup and view all the answers

### What is negation?

<p>The denial of a statement</p> Signup and view all the answers

### What are equivalent statements?

<p>Statements that are the same or equal the same thing</p> Signup and view all the answers

### Define perpendicular lines.

<p>Two lines that intersect to form right angles</p> Signup and view all the answers

### What is a bi-conditional statement?

<p>A statement defined to be true whenever both parts are true</p> Signup and view all the answers

### Explain deductive reasoning.

<p>A process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument</p> Signup and view all the answers

## Study Notes

### Algebraic Proofs Key Concepts

• Given: Represents the hypothesis in a mathematical statement, establishing conditions or assumptions to be considered.
• Prove: Refers to the conclusion drawn from logical reasoning and the given premises in a proof.

### Fundamental Properties

• Reflexive Property: States that any quantity is equal to itself (e.g., A = A).
• Symmetric Property: Indicates if A equals B, then B also equals A; equality is two-way.
• Transitive Property: Connects relationships; if A equals B and B equals C, then A equals C.
• Distributive Property: Describes how multiplication distributes over addition (e.g., A(B + C) = AB + AC).
• Substitution Property: Allows substitution of quantities for one another based on equality (if A = X, then replace A with X).
• Addition Property: States if A equals B, then adding the same term X to both equations preserves equality (A + X = B + X).
• Multiplication Property: If A equals B, then multiplying both sides by the same term equates them (A × X = B × X).
• Division Property: States that if A equals B, then dividing both sides by the same non-zero term keeps the equality (A / X = B / X).

### Reasoning Techniques

• Conjecture: A suggestion or statement believed to be true, inferred from examples, but not universally proven.
• Inductive Reasoning: Involves identifying patterns and making conjectures based on observed examples; often leads to unproven but plausible statements.
• Deductive Reasoning: Utilizes established facts, definitions, and logical principles to formulate valid arguments and proofs.

### Statement Forms

• Conditional Statement: Formulated as "If-Then"; comprises an hypothesis and a conclusion.
• Comverse: The result of reversing the hypothesis and conclusion of a conditional statement.
• Inverse: Developed by negating both the hypothesis and conclusion of a conditional statement.
• Contrapositive: Created by negating both the hypothesis and conclusion after switching them, forming a new statement based on the converse.

### More Definitions

• Negation: The opposite or denial of a given statement.
• Equivalent Statements: Statements that hold the same truth value, meaning they are interchangeable.
• Perpendicular Lines: Two lines that intersect to form right angles, confirming equivalence in their geometric properties.
• Bi-conditional Statement: Defined to be true if both constituent statements are true; functions as an "if and only if" condition.
• Hypothesis: The segment of a conditional statement following "if" but not including it.
• Conclusion: Follows "then" in a conditional statement, representing the result or outcome of the hypothesis.

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## Description

Test your understanding of important algebraic properties with these flashcards. Each card presents a key term and its definition, helping you to reinforce your knowledge of algebraic proofs. Perfect for students looking to excel in their algebra studies.

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