solution of question 27,28,29
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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Need solution of question 27,28,29
![### Logical Proof Problems and Statements
In this exercise, we explore a series of logical arguments, each requiring the construction of a formal proof. These problems involve logical reasoning using given statements and their corresponding justifications.
#### Problem 22
1. Expression to Prove:
\[
(a \rightarrow b) \rightarrow \sim p \rightarrow (r \lor s)
\]
2. Premises:
- \( a \rightarrow b \)
- \( p \rightarrow (r \lor s) \)
- \(\sim w \rightarrow (r \lor s)\)
- \(\sim p\)
3. Proof Steps:
- Step 1: \(a \rightarrow b\)
- Step 2: \((a \rightarrow b) \rightarrow \sim w\)
- Step 3: \(\sim w\)
- Step 4: \(\sim w \rightarrow (r \lor s)\)
- Step 5: \(r \lor s\)
- Step 6: \(p \rightarrow (r \lor s)\)
- Step 7: \(\sim p\)
#### Problem 23
1. Expression to Prove: \(c \rightarrow h\)
2. Premises:
- \((s \lor w) \rightarrow \sim d\)
- \(g \rightarrow (c \rightarrow h)\)
- \(\sim(s \lor w) \rightarrow g\)
- \(c \rightarrow h\)
3. Proof Steps:
- Step 1: \(d\)
- Step 2: \((s \lor w) \rightarrow \sim d\)
- Step 3: \(\sim(s \lor w)\)
- Step 4: \(\sim(s \lor w) \rightarrow g\)
- Step 5: \(g\)
- Step 6: \(g \rightarrow (c \rightarrow h)\)
- Step 7: \(c \rightarrow h\)
#### Problems 24-29
These are logical arguments, all valid, for which students are asked to construct formal proofs.
- **Problem 24**:
\[
r \rightarrow \sim s, \quad r \quad (\therefore \sim s)
\]
- **Problem 25**:
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50969b9e-0557-47b3-9c06-ed63c28b991b%2F25756fdc-a5c9-4796-a71a-9bf94e663baa%2Ft64xdw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Logical Proof Problems and Statements
In this exercise, we explore a series of logical arguments, each requiring the construction of a formal proof. These problems involve logical reasoning using given statements and their corresponding justifications.
#### Problem 22
1. Expression to Prove:
\[
(a \rightarrow b) \rightarrow \sim p \rightarrow (r \lor s)
\]
2. Premises:
- \( a \rightarrow b \)
- \( p \rightarrow (r \lor s) \)
- \(\sim w \rightarrow (r \lor s)\)
- \(\sim p\)
3. Proof Steps:
- Step 1: \(a \rightarrow b\)
- Step 2: \((a \rightarrow b) \rightarrow \sim w\)
- Step 3: \(\sim w\)
- Step 4: \(\sim w \rightarrow (r \lor s)\)
- Step 5: \(r \lor s\)
- Step 6: \(p \rightarrow (r \lor s)\)
- Step 7: \(\sim p\)
#### Problem 23
1. Expression to Prove: \(c \rightarrow h\)
2. Premises:
- \((s \lor w) \rightarrow \sim d\)
- \(g \rightarrow (c \rightarrow h)\)
- \(\sim(s \lor w) \rightarrow g\)
- \(c \rightarrow h\)
3. Proof Steps:
- Step 1: \(d\)
- Step 2: \((s \lor w) \rightarrow \sim d\)
- Step 3: \(\sim(s \lor w)\)
- Step 4: \(\sim(s \lor w) \rightarrow g\)
- Step 5: \(g\)
- Step 6: \(g \rightarrow (c \rightarrow h)\)
- Step 7: \(c \rightarrow h\)
#### Problems 24-29
These are logical arguments, all valid, for which students are asked to construct formal proofs.
- **Problem 24**:
\[
r \rightarrow \sim s, \quad r \quad (\therefore \sim s)
\]
- **Problem 25**:
\[
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