**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.

Name: **Mathematical Logic: Converse, Inverse, and Contrapositive Statement
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Description: **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.

We will use the following process: Statement If p, then q Converse If q, then p Inverse If…

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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)

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Statements and Logic

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

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**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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