Math Problem Statement
Question 1 (1 point) Let p and q denote false propositions. What is the truth value of the compound proposition below?
(p ∧ q) → ¬q
Question 1 options: True False
Solution
Let's analyze the given compound proposition:
Where:
- is false,
- is false,
- is the logical AND,
- is the negation of , which is true since is false.
Step-by-Step Breakdown:
- Evaluate : [ \text{Since both } p \text{ and } q \text{ are false, } p \land q \
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Math Problem Analysis
Mathematical Concepts
Propositional Logic
Logical Connectives
Truth Tables
Formulas
p ∧ q
¬q
(p ∧ q) → ¬q
Theorems
Implication (→) in Propositional Logic
Negation (¬)
Conjunction (∧)
Suitable Grade Level
College-level or Advanced High School