Discrete Mathematics - Rules of Inference

Questions and Answers

What is an argument?

A conclusion

A sequence of statements that end with a conclusion (correct)

An incorrect reasoning

None of the above

What does it mean for a conclusion to be valid?

A conclusion that must follow the truth of the preceding statements.

What are premises in an argument?

Proceeding statements.

What are fallacies?

Incorrect reasoning. Signup and view all the answers

What are rules of inference?

Simple argument forms. Signup and view all the answers

What is the Law of Detachment?

A tautology also known as Modus Ponens mode that affirms. Signup and view all the answers

Match the logical forms with their descriptions:

Modus Ponens = (p ∧ (p → q)) → q Modus Tollens = (¬q ∧ (p → q)) → ¬p Hypothetical Syllogism = ((p → q) ∧ (q → r)) → (p → r) Disjunctive Syllogism = ((p ∨ q) ∧ ¬p) → q Addition = p → (p ∨ q) Simplification = (p ∧ q) → p Conjunction = ((p) ∧ (q)) → (p ∧ q) Resolution = ((p ∨ q) ∧ (¬p ∨ r)) → (q ∨ r) Signup and view all the answers

Study Notes

Argument Fundamentals

An argument consists of a sequence of statements culminating in a conclusion.
Validity indicates that a conclusion necessarily follows from its preceding statements.

Key Components of Arguments

Premises are the preceding statements that support the conclusion.
Fallacies represent incorrect reasoning that undermines an argument's validity.

Rules of Inference

Rules of inference are basic argument structures that allow for the derivation of valid conclusions from given premises.

Specific Rules of Inference

Law of Detachment (Modus Ponens): If "p" is true and "p → q" is true, then "q" is necessarily true.
Example structure: If "p" and "p → q", then conclude "q".
Modus Tollens: If "¬q" (not q) is true and "p → q" is true, then "¬p" (not p) must also be true.
Example structure: If "¬q" and "p → q", then conclude "¬p".
Hypothetical Syllogism: If "p → q" and "q → r" are both true, then "p → r" is also true.
Example structure: If "p → q" and "q → r", then conclude "p → r".
Disjunctive Syllogism: From "p ∨ q" (either p or q) and "¬p" (not p), we can conclude "q".
Example structure: If "p ∨ q" and "¬p", then conclude "q".
Addition: If "p" is true, we can conclude "p ∨ q" (p or q).
Example structure: If "p", then conclude "p ∨ q".
Simplification: If "p ∧ q" (both p and q) is true, we can conclude "p".
Example structure: If "p ∧ q", then conclude "p".
Conjunction: If both "p" and "q" are true, we can form "p ∧ q".
Example structure: If "p" and "q", then conclude "p ∧ q".
Resolution: From "p ∨ q" and "¬p ∨ r", we can conclude "q ∨ r".
Example structure: If "p ∨ q" and "¬p ∨ r", then conclude "q ∨ r".

Description

Test your understanding of the foundational concepts in discrete mathematics with flashcards focused on rules of inference. This quiz covers essential terminology such as arguments, premises, and valid conclusions, helping you to strengthen your logical reasoning skills.