Let's break down the statement and identify the converse, contrapositive, and inverse based on the conditional provided:

The original statement is:

• If Kim received an A in her math class this past semester, then Kim received straight A's this past semester.

Definitions:

1. Converse: Swap the hypothesis and conclusion of the original statement.
2. Contrapositive: Negate both the hypothesis and conclusion, and then swap them.
3. Inverse: Negate both the hypothesis and conclusion, but keep them in the same order.

Applying these definitions:

1. Converse:

   • If Kim received straight A's this past semester, then Kim received an A in her math class this past semester.

2. Contrapositive:

   • If Kim did not receive straight A's this past semester, then Kim did not receive an A in her math class this past semester.

3. Inverse:

   • If Kim did not receive an A in her math class this past semester, then Kim did not receive straight A's this past semester.

You can now fill in these statements in the dropdowns.

Would you like further details on these concepts?

5 Related Questions:

1. What are the truth values of the converse, inverse, and contrapositive in relation to the original statement?
2. How can you verify if the contrapositive of a statement is logically equivalent to the original statement?
3. Can a conditional statement be true if the converse is false?
4. In what real-life scenarios might you apply contrapositive reasoning?
5. What is the significance of understanding inverse and converse in logical reasoning?

Tip: The contrapositive of a true statement is always true, while the converse and inverse may not be.