https://file.aiquickdraw.com/mathbot/file/1728551837750j5o2bpw1.jpg

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. \( (p \lor q) \Rightarrow ((p \land \neg q) \Leftrightarrow \neg p) \)

Here’s how to approach it:

### Steps for creating a truth table:
1. **Identify the variables**: In this case, we have two variables, \( p \) and \( q \).
2. **List all combinations of truth values**: There are 2 variables, so \( 2^2 = 4 \) rows in the truth table (combinations of True/False for \( p \) and \( q \)).
3. **Break the expression into parts**:
    - \( \neg p \)
    - \( \neg q \)
    - \( p \land \neg q \)
    - \( p \lor q \)
    - \( (p \land \neg q) \Leftrightarrow \neg p \)
    - \( (p \lor

Create a truth table for the given logical formulas.

This page provides step-by-step guidance on constructing truth tables for complex propositional logic formulas such as (p ∨ q) ⇒ ((p ∧ ¬q) ⇔ ¬p). Learn key concepts in logic, including implication, conjunction, and biconditional, with examples suitable for university-level discrete mathematics courses.

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