**Determine the truth value of $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$ when $p$ and $q$ and $r$ are False, and $s$ is True.**- [ ] True- [ ] False---To solve this, let's break it down step by step considering the given truth values:1. Evaluate $p \rightarrow q$: - Since both $p$ and $q$ are False, $p \rightarrow q$ is True (as False implies anything).2. Evaluate $q \rightarrow r$: - Since both $q$ and $r$ are False, $q \rightarrow r$ is True (as False implies anything).3. Now, evaluate $(p \rightarrow q) \lor (q \rightarrow r)$: - Both components are True, so the disjunction $(p \rightarrow q) \lor (q \rightarrow r)$ is True.4. Evaluate $r \rightarrow s$: - Since $r$ is False and $s$ is True, $r \rightarrow s$ is True (as False implies anything).5. Finally, evaluate $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$: - Both components are True, so the conjunction $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$ is True.Therefore, the truth value of the given expression is:- [x] True- [ ] False

Name: **Determine the truth value of $[(p \rightarrow q) \lor (q \rightarr
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Description: **Determine the truth value of \([(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$ when $p$ and $q$ and $r$ are False, and $s$ is True.**- [ ] True- [ ] False---To solve this, let's break it down step by step considering t

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Determine the truth value of [(p → q) v (q → r)] ^ (r → s) when p and q and r are False, and s is True.

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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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

**Determine the truth value of $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$ when $p$ and $q$ and $r$ are False, and $s$ is True.**

- [ ] True
- [ ] False

---

To solve this, let's break it down step by step considering the given truth values:

1. Evaluate $p \rightarrow q$:
- Since both $p$ and $q$ are False, $p \rightarrow q$ is True (as False implies anything).

2. Evaluate $q \rightarrow r$:
- Since both $q$ and $r$ are False, $q \rightarrow r$ is True (as False implies anything).

3. Now, evaluate $(p \rightarrow q) \lor (q \rightarrow r)$:
- Both components are True, so the disjunction $(p \rightarrow q) \lor (q \rightarrow r)$ is True.

4. Evaluate $r \rightarrow s$:
- Since $r$ is False and $s$ is True, $r \rightarrow s$ is True (as False implies anything).

5. Finally, evaluate $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$:
- Both components are True, so the conjunction $[(p \rightarrow q) \lor (q \rightarrow r)] \land (r \rightarrow s)$ is True.

Therefore, the truth value of the given expression is:
- [x] True
- [ ] False

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