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Questions and Answers
What is the truth value of the statement p → q if p is false and q is true?
What is the truth value of the statement p → q if p is false and q is true?
Which of the following is a property of if-then statements in propositional logic?
Which of the following is a property of if-then statements in propositional logic?
What is the contrapositive of the statement p → q?
What is the contrapositive of the statement p → q?
What can be inferred from the statements p → q and p?
What can be inferred from the statements p → q and p?
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What is the symbol used to denote the 'if-then' connective in propositional logic?
What is the symbol used to denote the 'if-then' connective in propositional logic?
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What is the truth value of the statement p → q if p is true and q is false?
What is the truth value of the statement p → q if p is true and q is false?
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Study Notes
Propositional Logic
- Definition: Propositional Logic is a branch of mathematics that deals with statements that can be either true (T) or false (F).
- Propositions: Statements that can be either true or false, denoted by p, q, r, etc.
-
Connectives: Symbols used to combine propositions, including:
- NOT (negation): ¬p (not p)
- AND (conjunction): p ∧ q (p and q)
- OR (disjunction): p ∨ q (p or q)
- IF-THEN (implication): p → q (if p, then q)
- IF AND ONLY IF (equivalence): p ⇔ q (p if and only if q)
If-Then Statements (Implication)
- Definition: An if-then statement is a proposition of the form "if p, then q", denoted by p → q.
- Meaning: If p is true, then q must also be true. If p is false, the statement is true regardless of the value of q.
- Truth Table:
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
-
Properties:
- Transitivity: If p → q and q → r, then p → r.
- Contrapositive: p → q is equivalent to ¬q → ¬p.
- Modus Ponens: If p → q and p, then q.
Propositional Logic
- Definition: Deals with statements that can be either true (T) or false (F)
- Propositions: Statements that can be either true or false, denoted by p, q, r, etc
Connectives
- NOT (negation): ¬p (not p)
- AND (conjunction): p ∧ q (p and q)
- OR (disjunction): p ∨ q (p or q)
- IF-THEN (implication): p → q (if p, then q)
- IF AND ONLY IF (equivalence): p ⇔ q (p if and only if q)
If-Then Statements (Implication)
- Definition: A proposition of the form "if p, then q", denoted by p → q
- Meaning: If p is true, then q must also be true; if p is false, the statement is true regardless of the value of q
- Truth Table: shows the possible combinations of p and q values and their corresponding implications
Properties of If-Then Statements
- Transitivity: If p → q and q → r, then p → r
- Contrapositive: p → q is equivalent to ¬q → ¬p
- Modus Ponens: If p → q and p, then q
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Description
Test your knowledge of Propositional Logic, including propositions, connectives, and logical operators. Understand the fundamentals of propositional logic, including negation, conjunction, disjunction, and implication.
