Mathematics 8 worksheet featuring logic exercises on inverse, converse, and contrapositive statements.

This worksheet is asking you to write the inverse, converse, and contrapositive of each given conditional statement.

Let’s first review what these terms mean:

Given a conditional statement:
> If P, then Q.

- Inverse: If not P, then not Q.
(Negate both the hypothesis and conclusion)

- Converse: If Q, then P.
(Swap the hypothesis and conclusion)

- Contrapositive: If not Q, then not P.
(Swap AND negate both parts — this is logically equivalent to the original statement)

---

Now let’s solve each problem one by one.

---

1. If you visited Dallas, then you’ve been to Texas.

- Inverse: If you did not visit Dallas, then you have not been to Texas.
*(Note: This is not necessarily true — you could go to Austin or Houston!)*

- Converse: If you’ve been to Texas, then you visited Dallas.
*(Also not necessarily true — many people visit Texas without going to Dallas.)*

- Contrapositive: If you have not been to Texas, then you did not visit Dallas.
*(This is logically true — if you never went to Texas, you couldn’t have visited Dallas, which is in Texas.)*

---

2. If m∠P = 90°, then ∠P is a right angle.

- Inverse: If m∠P ≠ 90°, then ∠P is not a right angle.
*(True — by definition, a right angle measures exactly 90°.)*

- Converse: If ∠P is a right angle, then m∠P = 90°.
*(True — again, this is the definition.)*

- Contrapositive: If ∠P is not a right angle, then m∠P ≠ 90°.
*(True — logically equivalent to the original.)*

---

3. If it is Saturday, then the school is closed.

- Inverse: If it is not Saturday, then the school is not closed.
*(Not necessarily true — school might be closed on Sunday, holidays, etc.)*

- Converse: If the school is closed, then it is Saturday.
*(Not necessarily true — school could be closed for other reasons.)*

- Contrapositive: If the school is not closed, then it is not Saturday.
*(Logically equivalent to original — if school is open, it can’t be Saturday, assuming the original statement is always true.)*

---

4. If an angle is a right angle, then it measures 90 degrees.

- Inverse: If an angle is not a right angle, then it does not measure 90 degrees.
*(True — only right angles measure 90°.)*

- Converse: If an angle measures 90 degrees, then it is a right angle.
*(True — this is the definition.)*

- Contrapositive: If an angle does not measure 90 degrees, then it is not a right angle.
*(True — logically equivalent to original.)*

---

5. If an animal is a dog, then it has four legs.

- Inverse: If an animal is not a dog, then it does not have four legs.
*(False — cats, horses, cows also have four legs.)*

- Converse: If an animal has four legs, then it is a dog.
*(False — again, many animals have four legs.)*

- Contrapositive: If an animal does not have four legs, then it is not a dog.
*(True — dogs always have four legs, so if it doesn’t, it can’t be a dog.)*

---

## ✔ Final Answers:

---

1. If you visited Dallas, then you’ve been to Texas.
- Inverse: If you did not visit Dallas, then you have not been to Texas.
- Converse: If you’ve been to Texas, then you visited Dallas.
- Contrapositive: If you have not been to Texas, then you did not visit Dallas.

---

2. If m∠P = 90°, then ∠P is a right angle.
- Inverse: If m∠P ≠ 90°, then ∠P is not a right angle.
- Converse: If ∠P is a right angle, then m∠P = 90°.
- Contrapositive: If ∠P is not a right angle, then m∠P ≠ 90°.

---

3. If it is Saturday, then the school is closed.
- Inverse: If it is not Saturday, then the school is not closed.
- Converse: If the school is closed, then it is Saturday.
- Contrapositive: If the school is not closed, then it is not Saturday.

---

4. If an angle is a right angle, then it measures 90 degrees.
- Inverse: If an angle is not a right angle, then it does not measure 90 degrees.
- Converse: If an angle measures 90 degrees, then it is a right angle.
- Contrapositive: If an angle does not measure 90 degrees, then it is not a right angle.

---

5. If an animal is a dog, then it has four legs.
- Inverse: If an animal is not a dog, then it does not have four legs.
- Converse: If an animal has four legs, then it is a dog.
- Contrapositive: If an animal does not have four legs, then it is not a dog.

---

📌 Note: The contrapositive is always logically equivalent to the original statement. The inverse and converse are not necessarily true unless the original is a biconditional (if and only if).

You can now fill these into your worksheet!

Good luck! 🍀
— Sir Tan