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:

(pq)¬q(p \land q) \rightarrow \neg q

Where:

  • pp is false,
  • qq is false,
  • \land is the logical AND,
  • ¬q\neg q is the negation of qq, which is true since qq is false.

Step-by-Step Breakdown:

  1. Evaluate pqp \land q: [ \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