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Write your own example of a conditional statement. Then write the converse of your conditional statement.

After you have posted your conditional statement and its converse, respond to two of your classmates’ posts. In your response to each post:

Write the inverse and contrapositive of a classmate’s conditional statement.

Determine the validity of all the statements, explaining your reasoning in each case.

1 answer

Conditional Statement: If it rains, then the ground will be wet.

Converse: If the ground is wet, then it rained.

Responses to Classmates

Classmate A's Statement: Conditional Statement: If I exercise regularly, then I feel healthier.

Inverse: If I do not exercise regularly, then I do not feel healthier.

Contrapositive: If I do not feel healthier, then I do not exercise regularly.

Validity of Statements:

  1. Conditional Statement: This is often valid because regular exercise is linked to better health.
  2. Inverse: This may not always be valid since there are people who might not exercise yet still feel healthy due to other factors such as diet or genetics.
  3. Contrapositive: This statement is logically valid because if one does not feel healthier, it could suggest they aren't exercising regularly; however, other factors can also contribute to how a person feels.

Classmate B's Statement: Conditional Statement: If a person is a teenager, then they are in high school.

Inverse: If a person is not a teenager, then they are not in high school.

Contrapositive: If a person is not in high school, then they are not a teenager.

Validity of Statements:

  1. Conditional Statement: This statement is generally valid but not definitive since some teenagers might not be in high school if they have graduated early or are being homeschooled.
  2. Inverse: This is not valid; there are many individuals who are not teenagers who are still in high school.
  3. Contrapositive: This too is invalid; just because someone is not in high school doesn't mean they aren't a teenager; they might be in middle school.

Conclusion: Each statement has a varying degree of validity based on the definitions and the factual relationships involved.