Write the converse, inoverse, andNi contrapositive of the following statement: the train is late, then I am in class on fime. If not

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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.
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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