Converse, Inverse, Contrapositive | Worksheet 6/10

Question 1

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 2

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 3

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 4

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 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 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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 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 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

Converse, Inverse, Contrapositive: Worksheet 6 - Intermediate-Advanced Practice Converse, Inverse, Contrapositive INTERMEDIATE ADVANCED

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20