Math Problem Statement

Create a truth table for the given logical formulas.

Solution

The image contains a list of logical expressions, and the task is to create truth tables for these formulas. To proceed, I'll explain how to create a truth table for one of these formulas, step by step. Let's start with formula number 1:

  1. (pq)((p¬q)¬p)(p \lor q) \Rightarrow ((p \land \neg q) \Leftrightarrow \neg p)

Here’s how to approach it:

Steps for creating a truth table:

  1. Identify the variables: In this case, we have two variables, pp and qq.
  2. List all combinations of truth values: There are 2 variables, so 22=42^2 = 4 rows in the truth table (combinations of True/False for pp and qq).
  3. Break the expression into parts:
    • ¬p\neg p
    • ¬q\neg q
    • p¬qp \land \neg q
    • pqp \lor q
    • (p¬q)¬p(p \land \neg q) \Leftrightarrow \neg p
    • ( (p \lor

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Math Problem Analysis

Mathematical Concepts

Logic
Propositional Logic
Truth Tables

Formulas

(p ∨ q) ⇒ ((p ∧ ¬q) ⇔ ¬p)
(p ⇒ q) ⇔ (¬p ∨ q)
(p ∧ ¬q) ∨ (¬p ∧ q)

Theorems

Implication (⇒)
Biconditional (⇔)
De Morgan's Laws

Suitable Grade Level

University Level - Discrete Mathematics