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Write the convers If you visit your g

Write the convers If you visit your g

Advanced Engineering Mathematics
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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**Title: Understanding Converse, Inverse, and Contrapositive Statements** **Instructions:** Write the converse, inverse, and contrapositive of the statement: "If you visit your grandparents, then you can go to the park." **Detailed Explanation:** When working with conditional statements in logic, it’s important to understand the different transformations that can be created from a given statement. We will explore the converse, inverse, and contrapositive of the provided statement: 1. **Original Statement (Conditional):** "If you visit your grandparents, then you can go to the park." 2. **Converse:** The converse of a statement is formed by reversing the hypothesis and conclusion. - **Converse Statement:** "If you can go to the park, then you visit your grandparents." 3. **Inverse:** The inverse of a statement is formed by negating both the hypothesis and the conclusion. - **Inverse Statement:** "If you do not visit your grandparents, then you cannot go to the park." 4. **Contrapositive:** The contrapositive of a statement is formed by both reversing and negating the hypothesis and the conclusion. - **Contrapositive Statement:** "If you cannot go to the park, then you do not visit your grandparents." **Note:** Understanding these transformations helps in examining and validating logical relationships in diverse fields like mathematics, computer science, and critical thinking. For further practice, try creating your own statements and apply these transformations to see how they change the logical structure!
Transcribed Image Text:**Title: Understanding Converse, Inverse, and Contrapositive Statements** **Instructions:** Write the converse, inverse, and contrapositive of the statement: "If you visit your grandparents, then you can go to the park." **Detailed Explanation:** When working with conditional statements in logic, it’s important to understand the different transformations that can be created from a given statement. We will explore the converse, inverse, and contrapositive of the provided statement: 1. **Original Statement (Conditional):** "If you visit your grandparents, then you can go to the park." 2. **Converse:** The converse of a statement is formed by reversing the hypothesis and conclusion. - **Converse Statement:** "If you can go to the park, then you visit your grandparents." 3. **Inverse:** The inverse of a statement is formed by negating both the hypothesis and the conclusion. - **Inverse Statement:** "If you do not visit your grandparents, then you cannot go to the park." 4. **Contrapositive:** The contrapositive of a statement is formed by both reversing and negating the hypothesis and the conclusion. - **Contrapositive Statement:** "If you cannot go to the park, then you do not visit your grandparents." **Note:** Understanding these transformations helps in examining and validating logical relationships in diverse fields like mathematics, computer science, and critical thinking. For further practice, try creating your own statements and apply these transformations to see how they change the logical structure!
### Identifying Logical Statements This exercise requires identifying the converse and inverse statements related to a given conditional statement. #### Original Conditional Statement: - **If you can go to the park, then you visit your grandparents.** #### Task: Identify the Converse Statement. A converse statement is created by switching the hypothesis and conclusion of the original conditional statement. Options: 1. **A.** If you cannot go to the park, then you did not visit your grandparents. 2. **B.** If you can go to the park, then you visit your grandparents. 3. **C.** If you cannot go to the park, then you visit your grandparents. 4. **D.** If you did not visit your grandparents, then you cannot go to the park. **Answer: D.** If you visit your grandparents, then you can go to the park. #### Task: Identify the Inverse Statement. An inverse statement is created by negating both the hypothesis and the conclusion of the original conditional statement. Options: 1. **A.** If you cannot go to the park, then you did not visit your grandparents. 2. **B.** If you did not visit your grandparents, then you cannot go to the park. 3. **C.** If you cannot go to the park, then you visit your grandparents. 4. **D.** If you did not visit your grandparents, then you cannot go to the park. **Answer: A.** If you cannot go to the park, then you do not visit your grandparents. This exercise assists in understanding logical relationships and the formulation of converse and inverse statements in conditional logic.
Transcribed Image Text:### Identifying Logical Statements This exercise requires identifying the converse and inverse statements related to a given conditional statement. #### Original Conditional Statement: - **If you can go to the park, then you visit your grandparents.** #### Task: Identify the Converse Statement. A converse statement is created by switching the hypothesis and conclusion of the original conditional statement. Options: 1. **A.** If you cannot go to the park, then you did not visit your grandparents. 2. **B.** If you can go to the park, then you visit your grandparents. 3. **C.** If you cannot go to the park, then you visit your grandparents. 4. **D.** If you did not visit your grandparents, then you cannot go to the park. **Answer: D.** If you visit your grandparents, then you can go to the park. #### Task: Identify the Inverse Statement. An inverse statement is created by negating both the hypothesis and the conclusion of the original conditional statement. Options: 1. **A.** If you cannot go to the park, then you did not visit your grandparents. 2. **B.** If you did not visit your grandparents, then you cannot go to the park. 3. **C.** If you cannot go to the park, then you visit your grandparents. 4. **D.** If you did not visit your grandparents, then you cannot go to the park. **Answer: A.** If you cannot go to the park, then you do not visit your grandparents. This exercise assists in understanding logical relationships and the formulation of converse and inverse statements in conditional logic.
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