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Questions and Answers
Which logical operator is used to denote negation?
The conjunction operator (∧) is true if both propositions are false.
False
What is the definition of a disjunction?
The disjunction of propositions p and q, denoted by p ∨ q, is true when at least one of the propositions is true.
In a conjunction, both statements must be ______ for the entire statement to be true.
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What logical connective is represented by the symbol →?
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What is the truth table for a conjunction?
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Study Notes
Compound Propositions
- Comprise two or more propositions linked by logical connectors.
- Enable the creation of new propositions using existing ones.
Logical Operators/Connectives
- Functions to form new propositions from multiple existing propositions.
- Precedence order of logical operators includes:
- Negation (¬)
- Conjunction (∧)
- Disjunction (∨)
- Implication (→)
- Biconditional (↔)
Negation
- Represents the opposite of a given statement.
- Forms a new proposition from a single proposition.
- Truth table indicates:
- If p is true (T), ¬p is false (F).
- If p is false (F), ¬p is true (T).
- Example:
- p: "Azam is a doctor."
- ¬p: "Azam is not a doctor."
Conjunction
- Defines the logical "and", denoted as p ∧ q.
- True only when both propositions p and q are true; false otherwise.
- Truth table shows:
- T ∧ T = T
- T ∧ F = F
- F ∧ T = F
- F ∧ F = F
- Example:
- p: "Rebecca’s PC has more than 16 GB free hard disk space."
- q: "The processor in Rebecca’s PC runs faster than 1 GHz."
- Conjunction p ∧ q: Both conditions must be true.
Disjunction
- Represents the logical "or", denoted as p ∨ q.
- False only when both propositions p and q are false; true otherwise.
- Truth table indicates:
- T ∨ T = T
- T ∨ F = T
- F ∨ T = T
- F ∨ F = F
- Example:
- p: "Rebecca’s PC has more than 16 GB free hard disk space."
- q: "The processor in Rebecca’s PC runs faster than 1 GHz."
- Disjunction p ∨ q: At least one of the conditions must be true.
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Description
This quiz explores the formation and structure of compound propositions using logical operators such as negation, conjunction, and disjunction. Test your understanding of how these connectives work and their precedence in logical reasoning. Perfect for those studying foundational concepts in logic.
