Logic worksheet focusing on identifying inverse, converse, and contrapositive of if-then statements.

Here are the solutions to your worksheet.

Part I: Determine if each statement is the inverse, converse, or contrapositive.

First Statement: "If you study hard, then your scores will improve."
* P (Hypothesis): You study hard.
* Q (Conclusion): Your scores will improve.

1. "If your scores improved, then you studied hard."
* This switches the order ($q \rightarrow p$).
* Answer: Converse

2. "If you do not study hard, then your scores will not improve."
* This negates both parts but keeps the order ($\sim p \rightarrow \sim q$).
* Answer: Inverse

3. "If your scores did not improve, then you did not study hard."
* This switches the order and negates both parts ($\sim q \rightarrow \sim p$).
* Answer: Contrapositive

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Second Statement: "If an angle measures $90^\circ$, then it is called a right angle."
* P (Hypothesis): An angle measures $90^\circ$.
* Q (Conclusion): It is called a right angle.

4. "If an angle doesn't measure $90^\circ$, then it is not called a right angle."
* This negates both parts but keeps the order ($\sim p \rightarrow \sim q$).
* Answer: Inverse

5. "If an angle is not called a right angle, then it doesn't measure $90^\circ$."
* This switches the order and negates both parts ($\sim q \rightarrow \sim p$).
* Answer: Contrapositive

6. "If an angle is called a right angle, then it measures $90^\circ$."
* This switches the order ($q \rightarrow p$).
* Answer: Converse

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Part II: Transform the given statements.

Statement 1: "If you are patient and persistent, then you will succeed."

* Inverse (Negate both parts): If you are not patient and persistent, then you will not succeed.
* Converse (Switch the parts): If you succeed, then you are patient and persistent.
* Contrapositive (Switch and negate both parts): If you do not succeed, then you are not patient and persistent.

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Statement 2: "If a triangle is equilateral, then it is equiangular."

* Inverse (Negate both parts): If a triangle is not equilateral, then it is not equiangular.
* Converse (Switch the parts): If a triangle is equiangular, then it is equilateral.
* Contrapositive (Switch and negate both parts): If a triangle is not equiangular, then it is not equilateral.

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Final Answer:

I. Directions:
1. Converse
2. Inverse
3. Contrapositive
4. Inverse
5. Contrapositive
6. Converse

II. Directions:

| IF-THEN STATEMENT | INVERSE | CONVERSE | CONTRAPOSITIVE |
| :--- | :--- | :--- | :--- |
| If you are patient and persistent, then you will succeed. | If you are not patient and persistent, then you will not succeed. | If you succeed, then you are patient and persistent. | If you do not succeed, then you are not patient and persistent. |
| If a triangle is equilateral, then it is equiangular. | If a triangle is not equilateral, then it is not equiangular. | If a triangle is equiangular, then it is equilateral. | If a triangle is not equiangular, then it is not equilateral. |