Write the converse, inoverse, andNi contrapositive of the following statement: the train is late, then I am in class on fime. If not
Write the converse, inoverse, andNi contrapositive of the following statement: the train is late, then I am in class on fime. If not
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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
Transcribed Image Text:**Mathematical Logic: Converse, Inverse, and Contrapositive Statements**
**Original Statement:**
"If the train is late, then I am not in class on time."
**Task:**
Write the converse, inverse, and contrapositive of the given statement.
**Definitions:**
1. **Converse**: The statement formed by swapping the hypothesis and conclusion.
- **Converse Statement**: "If I am not in class on time, then the train is late."
2. **Inverse**: The statement formed by negating both the hypothesis and conclusion.
- **Inverse Statement**: "If the train is not late, then I am in class on time."
3. **Contrapositive**: The statement formed by both swapping and negating the hypothesis and conclusion.
- **Contrapositive Statement**: "If I am in class on time, then the train is not late."
Understanding these logical transformations is essential in mathematical reasoning and can help in proving the equivalence of statements.
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