3) j - i -j → k ~k .. i
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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3rd question
Transcribed Image Text:# Logical Reasoning Exercise
**Instructions:** In 1–4, assign truth values to the variables to make the premises true. Then, demonstrate that the arguments are valid by showing that true premises must lead to a true conclusion.
**Exercise:**
1. **Problem 1:**
Premises:
- \( p \rightarrow q \)
- \( q \rightarrow r \)
- \( p \)
Conclusion:
- ∴ \( r \)
2. **Problem 2:**
Premises:
- \( a \lor b \)
- \( b \rightarrow \sim c \)
- \( c \)
Conclusion:
- ∴ \( a \)
3. **Problem 3:**
Premises:
- \( j \rightarrow i \)
- \( \sim j \rightarrow k \)
- \( \sim k \)
Conclusion:
- ∴ \( i \)
4. **Problem 4:**
Premises:
- \( d \land \sim h \)
- \( h \lor y \)
- \( y \rightarrow n \)
Conclusion:
- ∴ \( n \)
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