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Consider the following statement. If you are the president of the United States, then your age is at least 35. (a) Write the converse of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States. (b) Write the inverse of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States. (c) Write the contrapositive of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States.

Consider the following statement. If you are the president of the United States, then your age is at least 35. (a) Write the converse of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States. (b) Write the inverse of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States. (c) Write the contrapositive of the given statement. If you are not the president of the United States, then your age is less than 35. If your age is less than 35, then you are the president of the United States. If you are the president of the United States, then your age is less than 35. If your age is at least 35, then you are the president of the United States. If you are not the president of the United States, then your age is at least 35. If your age is less than 35, then you are not the president of the United States.

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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**Interactive Exercise: Logical Statements** **Consider the following statement:** "If you are the president of the United States, then your age is at least 35." --- ### (a) Write the converse of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. ### (b) Write the inverse of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. ### (c) Write the contrapositive of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. --- **Instructions:** Choose the appropriate option for each logical transformation (converse, inverse, contrapositive) of the given statement.
Transcribed Image Text:**Interactive Exercise: Logical Statements** **Consider the following statement:** "If you are the president of the United States, then your age is at least 35." --- ### (a) Write the converse of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. ### (b) Write the inverse of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. ### (c) Write the contrapositive of the given statement. - ○ If you are not the president of the United States, then your age is less than 35. - ○ If your age is less than 35, then you are the president of the United States. - ○ If you are the president of the United States, then your age is less than 35. - ○ If your age is at least 35, then you are the president of the United States. - ○ If you are not the president of the United States, then your age is at least 35. - ○ If your age is less than 35, then you are not the president of the United States. --- **Instructions:** Choose the appropriate option for each logical transformation (converse, inverse, contrapositive) of the given statement.
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