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Questions and Answers
What is the definition of disjunction?
What is the definition of disjunction?
- True if both P and Q have the same truth value.
- Only false if P is true and Q is false.
- True if P or Q is true, but false if both are false. (correct)
- True only if both P and Q are true.
Which statement is true regarding a biconditional statement?
Which statement is true regarding a biconditional statement?
- It is true if both P and Q are true or both are false. (correct)
- It is false only if one of P or Q is true.
- It is true if P and Q have different truth values.
- It indicates a direct cause and effect relationship.
What characterizes an exclusive OR operation?
What characterizes an exclusive OR operation?
- True if both P and Q are false.
- Only false when both P and Q are false.
- True only if both P and Q are true.
- True if either P or Q is true, but not both. (correct)
What does a conditional statement imply?
What does a conditional statement imply?
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What does negation represent?
What does negation represent?
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Study Notes
Logical Operations in Propositional Logic
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Negation (¬p)
- Represents "It is not the case that P" or "Not P."
- Changes the truth value of proposition P to its opposite.
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Conjunction (p ∧ q)
- Denotes "P and Q."
- The statement is only true when both P and Q are true.
Truth Conditions for Logical Operations
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Disjunction (p ∨ q)
- Indicates "P or Q."
- This operation is only false when both P and Q are false.
-
Exclusive Or (p ⊕ q)
- Described as "Either P or Q, but not both."
- The outcome is true when one of them is true (TF or FT) and false when they share the same truth values (TT or FF).
Implications and Equivalences
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Conditional Statement (p → q)
- Represents "If P then Q."
- This statement is false only when P is true and Q is false (TF).
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Biconditional Statement (p ↔ q)
- Expresses "P if and only if Q."
- True when both P and Q have the same truth values, either both true (TT) or both false (FF).
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