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Converse, Inverse, Contrapositive: Worksheet 10 - Expert Practice Converse, Inverse, Contrapositive EXPERT

Ready to master Converse, Inverse, Contrapositive? This accuracy focus 👑 worksheet (10/10) presents 20 expert-level challenges. Focus area: application-based learning. Learn to solve converse, inverse, contrapositive reasoning tricks, handle fast converse, inverse, contrapositive solving, and perfect converse, inverse, contrapositive mastery with our step-by-step solutions.

📝 Worksheet 10 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Converse, Inverse, Contrapositive
Worksheet 10 of 10 (100% complete)

Question 1

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If a number is divisible by 4 is false, then it is even is false

Question 2

Given the conditional statement: "If you study hard, then you will pass" (p → q) What is the Converse of this statement?
Step 1: Understand the original statement
Original: p → q means "If you study hard, then you will pass"

Step 2: Understand Converse
Converse switches the hypothesis and conclusion: q → p
If the original is p → q, the converse is q → p

Step 3: Apply to our statement
Converse: If you will pass, then you study hard

Question 3

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If it is even is false, then a number is divisible by 4 is false

Question 4

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If it is even is false, then a number is divisible by 4 is false

Question 5

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Converse of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Converse
Converse switches the hypothesis and conclusion: q → p
If the original is p → q, the converse is q → p

Step 3: Apply to our statement
Converse: If I wake up, then the alarm rings

Question 6

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Converse of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Converse
Converse switches the hypothesis and conclusion: q → p
If the original is p → q, the converse is q → p

Step 3: Apply to our statement
Converse: If it is even, then a number is divisible by 4

Question 7

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If I wake up is false, then the alarm rings is false

Question 8

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If I wake up is false, then the alarm rings is false

Question 9

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If the alarm rings is false, then I wake up is false

Question 10

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If a number is divisible by 4 is false, then it is even is false

Question 11

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Converse of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Converse
Converse switches the hypothesis and conclusion: q → p
If the original is p → q, the converse is q → p

Step 3: Apply to our statement
Converse: If I wake up, then the alarm rings

Question 12

Given the conditional statement: "If you study hard, then you will pass" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If you study hard, then you will pass"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If you study hard is false, then you will pass is false

Question 13

Given the conditional statement: "If you study hard, then you will pass" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If you study hard, then you will pass"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If you will pass is false, then you study hard is false

Question 14

Given the conditional statement: "If you study hard, then you will pass" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If you study hard, then you will pass"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If you will pass is false, then you study hard is false

Question 15

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If it is raining, then the ground is wet"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If it is raining is false, then the ground is wet is false

Question 16

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If I wake up is false, then the alarm rings is false

Question 17

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Inverse of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Inverse
Inverse negates both parts: ¬p → ¬q
If the original is p → q, the inverse is ¬p → ¬q

Step 3: Apply to our statement
Inverse: If the alarm rings is false, then I wake up is false

Question 18

Given the conditional statement: "If a number is divisible by 4, then it is even" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If a number is divisible by 4, then it is even"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If it is even is false, then a number is divisible by 4 is false

Question 19

Given the conditional statement: "If the alarm rings, then I wake up" (p → q) What is the Converse of this statement?
Step 1: Understand the original statement
Original: p → q means "If the alarm rings, then I wake up"

Step 2: Understand Converse
Converse switches the hypothesis and conclusion: q → p
If the original is p → q, the converse is q → p

Step 3: Apply to our statement
Converse: If I wake up, then the alarm rings

Question 20

Given the conditional statement: "If you study hard, then you will pass" (p → q) What is the Contrapositive of this statement?
Step 1: Understand the original statement
Original: p → q means "If you study hard, then you will pass"

Step 2: Understand Contrapositive
Contrapositive switches AND negates both parts: ¬q → ¬p
If the original is p → q, the contrapositive is ¬q → ¬p
Important: A conditional and its contrapositive are LOGICALLY EQUIVALENT

Step 3: Apply to our statement
Contrapositive: If you will pass is false, then you study hard is false
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