**Constructing a Truth Table for the Statement \( \sim p \leftrightarrow (p \lor q) \)**In this task, we aim to complete the truth table for the given logical statement \( \sim p \leftrightarrow (p \lor q) \).A truth table details the outcomes of logical expressions based on the truth values of their variables. Let's examine and fill out the table step-by-step.### Truth Table Explanation:The columns of the table represent the following:- \( p \) and \( q \): The primary variables which each can be either True (T) or False (F).- \( p \lor q \): The logical OR operation between \( p \) and \( q \).- \( \sim p \leftrightarrow (p \lor q) \): The equivalence between the negation of \( p \) and the expression \( (p \lor q) \).Here is the structure of the truth table that needs to be completed:| \( p \) | \( q \) | \( p \lor q \) | \( \sim p \leftrightarrow (p \lor q) \) ||:-------:|:-------:|:--------------:|:---------------------------------------:|| T | T | \(\downarrow\) | \(\downarrow\) || T | F | \(\downarrow\) | \(\downarrow\) || F | T | \(\downarrow\) | \(\downarrow\) || F | F | \(\downarrow\) | \(\downarrow\) |**Steps to Complete the Table:**1. **Evaluate \( p \lor q \)**: - If either \( p \) or \( q \) (or both) is true, \( p \lor q \) is true (T). - If both \( p \) and \( q \) are false, \( p \lor q \) is false (F).2. **Evaluate \( \sim p \)**: - True if \( p \) is false. - False if \( p \) is true.3. **Evaluate \( \sim p \leftrightarrow

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Math

Advanced Math

Construct a truth table for the statement p<(pvq). Complete the truth table. q pvq -p+(pvq) T T T F F T F F at Р

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Constructing a Truth Table for the Statement \( \sim p \leftrightarrow (p \lor q) \)**

In this task, we aim to complete the truth table for the given logical statement \( \sim p \leftrightarrow (p \lor q) \).

A truth table details the outcomes of logical expressions based on the truth values of their variables. Let's examine and fill out the table step-by-step.

<img src="image_url" alt="Truth table for the statement ~p↔(p∨q)">

### Truth Table Explanation:

The columns of the table represent the following:
- \( p \) and \( q \): The primary variables which each can be either True (T) or False (F).
- \( p \lor q \): The logical OR operation between \( p \) and \( q \).
- \( \sim p \leftrightarrow (p \lor q) \): The equivalence between the negation of \( p \) and the expression \( (p \lor q) \).

Here is the structure of the truth table that needs to be completed:

| \( p \) | \( q \) | \( p \lor q \) | \( \sim p \leftrightarrow (p \lor q) \) |
|:-------:|:-------:|:--------------:|:---------------------------------------:|
| T | T | \(\downarrow\) | \(\downarrow\) |
| T | F | \(\downarrow\) | \(\downarrow\) |
| F | T | \(\downarrow\) | \(\downarrow\) |
| F | F | \(\downarrow\) | \(\downarrow\) |

**Steps to Complete the Table:**
1. **Evaluate \( p \lor q \)**:
- If either \( p \) or \( q \) (or both) is true, \( p \lor q \) is true (T).
- If both \( p \) and \( q \) are false, \( p \lor q \) is false (F).

2. **Evaluate \( \sim p \)**:
- True if \( p \) is false.
- False if \( p \) is true.

3. **Evaluate \( \sim p \leftrightarrow

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