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Converse, Inverse, Contrapositive Beginner-Intermediate Worksheet: Focus on common variations practice Converse, Inverse, Contrapositive BEGINNER INTERMEDIATE

Level up your Converse, Inverse, Contrapositive skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: converse, inverse, contrapositive for competitive exams, how to solve converse, inverse, contrapositive, converse, inverse, contrapositive tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:
Your progress through Converse, Inverse, Contrapositive
Worksheet 4 of 10 (33% complete)

Question 1

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Converse 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 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 the ground is wet, then it is raining

Question 2

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Converse 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 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 the ground is wet, then it is raining

Question 3

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 4

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Contrapositive 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 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 the ground is wet is false, then it is raining is false

Question 5

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 6

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 7

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 8

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 9

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Contrapositive 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 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 the ground is wet is false, then it is raining is false

Question 10

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 11

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 12

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 13

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Converse 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 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 the ground is wet, then it is raining

Question 14

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 15

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 16

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 17

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 18

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Converse 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 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 the ground is wet, then it is raining

Question 19

Given the conditional statement: "If it is raining, then the ground is wet" (p → q) What is the Converse 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 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 the ground is wet, then it is raining

Question 20

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
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