**Construct a Truth Table for the Given Statement**Statement: \( q \leftrightarrow \neg p \)**Fill in the Truth Table:**The truth table consists of the following columns:- **p**: Represents the truth value of proposition \( p \). Can be either True (T) or False (F).- **q**: Represents the truth value of proposition \( q \). Can be either True (T) or False (F).- **\(\neg p\)**: Represents the negation of \( p \).- **\(q \leftrightarrow \neg p\)**: Represents the biconditional statement, which is true if both \( q \) and \(\neg p\) have the same truth value.| p | q | \(\neg p\) | \(q \leftrightarrow \neg p\) ||---|---|-----------|------------------------------|| T | T | | || T | F | | || F | T | | || F | F | | |

Answered: Construct a truth table for the given…

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

**Construct a Truth Table for the Given Statement**

Statement: \( q \leftrightarrow \neg p \)

**Fill in the Truth Table:**

The truth table consists of the following columns:

- **p**: Represents the truth value of proposition \( p \). Can be either True (T) or False (F).
- **q**: Represents the truth value of proposition \( q \). Can be either True (T) or False (F).
- **\(\neg p\)**: Represents the negation of \( p \).
- **\(q \leftrightarrow \neg p\)**: Represents the biconditional statement, which is true if both \( q \) and \(\neg p\) have the same truth value.

| p | q | \(\neg p\) | \(q \leftrightarrow \neg p\) |
|---|---|-----------|------------------------------|
| T | T | | |
| T | F | | |
| F | T | | |
| F | F | | |

Expert Solution

Step 1

Truth table:

The truth table is a tabular view of all combinations of values for the inputs and their corresponding outputs. It is a mathematical table that shows all possible results that may be occur from all possible scenarios. It is used for logic tasks such as logic algebra and electronic circuits.

Negation:

In logic, negation, also called the logical complement, is an operation that takes a proposition to another proposition "not ", written, or. It is interpreted intuitively as being true when is false, and false when is true. Negation is thus a unary logical connective.

if and only if:

In logic and related fields such as mathematics and philosophy, " if and only if " (shortened as " iff ") is a biconditional logical connective between statements, where either both statements are true or both are false.