Construct a truth table for the given statement. ~p->q ### Constructing a Truth Table for the Given Statement**Statement:**\[ \neg p \rightarrow q \]**Instructions:**Fill in the truth table.**Truth Table:**|| p | q | $\neg p$ | $\neg p \rightarrow q$ ||:-:|:-:|:-:|:-:|| T | T | ▼ | ▼ || T | F | ▼ | ▼ || F | T | ▼ | ▼ || F | F | ▼ | ▼ |**Explanation:**- **p**: Represents the first proposition which can either be True (T) or False (F).- **q**: Represents the second proposition which can either be True (T) or False (F).- **$\neg p$**: Represents the negation of the proposition $p$.- **$\neg p \rightarrow q$**: Represents a conditional statement where the antecedent is $\neg p$ and the consequent is $q$.For each combination of values of $p$ and $q$, you need to determine the truth values of $\neg p$ and $\neg p \rightarrow q$:1. Determine $\neg p$: - If $p$ is True (T), then $\neg p$ is False (F). - If $p$ is False (F), then $\neg p$ is True (T).2. Determine $\neg p \rightarrow q$: - Use the truth table for the conditional statement $A \rightarrow B$: - If A is True and B is True, then $A \rightarrow B$ is True (T). - If A is True and B is False, then $A \rightarrow B$ is False (F). - If A is False, then $A \rightarrow B$ is True (T) regardless of B.Fill in the table accordingly by determining the values step by step for each row.**Note:** Each row of the table represents a unique combination of truth values for the propositions $p$ and $q$.

The logical operator '~' means negation. This means that the truth value changes to false and the…

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Construct a truth table for the given statement. -p→q Fill in the truth table. b. -p

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.

~p->q

### Constructing a Truth Table for the Given Statement

**Statement:**

\[ \neg p \rightarrow q \]

**Instructions:**

Fill in the truth table.

**Truth Table:**

|
| p | q | $\neg p$ | $\neg p \rightarrow q$ |
|:-:|:-:|:-:|:-:|
| T | T | ▼ | ▼ |
| T | F | ▼ | ▼ |
| F | T | ▼ | ▼ |
| F | F | ▼ | ▼ |

**Explanation:**

- **p**: Represents the first proposition which can either be True (T) or False (F).
- **q**: Represents the second proposition which can either be True (T) or False (F).
- **$\neg p$**: Represents the negation of the proposition $p$.
- **$\neg p \rightarrow q$**: Represents a conditional statement where the antecedent is $\neg p$ and the consequent is $q$.

For each combination of values of $p$ and $q$, you need to determine the truth values of $\neg p$ and $\neg p \rightarrow q$:

1. Determine $\neg p$:
- If $p$ is True (T), then $\neg p$ is False (F).
- If $p$ is False (F), then $\neg p$ is True (T).

2. Determine $\neg p \rightarrow q$:
- Use the truth table for the conditional statement $A \rightarrow B$:
- If A is True and B is True, then $A \rightarrow B$ is True (T).
- If A is True and B is False, then $A \rightarrow B$ is False (F).
- If A is False, then $A \rightarrow B$ is True (T) regardless of B.

Fill in the table accordingly by determining the values step by step for each row.

**Note:** Each row of the table represents a unique combination of truth values for the propositions $p$ and $q$.

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