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Complex Logical Inference - Intermediate Level: tricky scenarios handling Complex Logical Inference INTERMEDIATE

This expert challenge 📈 worksheet focuses on Complex Logical Inference - a key topic in Inference. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve complex logical inference, complex logical inference tricks, and complex logical inference shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Complex Logical Inference
Worksheet 5 of 10 (44% complete)

Question 1

Given these logical premises: • If P, then Q • If Q, then R • If R, then S • Not S Which statement must be true?
This requires multi-step logical deduction:
• If P, then Q
• If Q, then R
• If R, then S
• Not S

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Not P

Question 2

Given these logical premises: • All successful people work hard • Some hard workers are lucky • No lazy people are successful • John is successful Which statement must be true?
This requires multi-step logical deduction:
• All successful people work hard
• Some hard workers are lucky
• No lazy people are successful
• John is successful

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: John works hard

Question 3

Given these logical premises: • If P, then Q • If Q, then R • If R, then S • Not S Which statement must be true?
This requires multi-step logical deduction:
• If P, then Q
• If Q, then R
• If R, then S
• Not S

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Not P

Question 4

Given these logical premises: • If A, then B • If B, then C • If C, then not D • A is true Which statement must be true?
This requires multi-step logical deduction:
• If A, then B
• If B, then C
• If C, then not D
• A is true

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: D is false

Question 5

Given these logical premises: • If it's a weekday, I work • If I work, I get tired • If I'm tired, I sleep early • I didn't sleep early Which statement must be true?
This requires multi-step logical deduction:
• If it's a weekday, I work
• If I work, I get tired
• If I'm tired, I sleep early
• I didn't sleep early

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: It's not a weekday

Question 6

Given these logical premises: • Every cat is a mammal • No mammal can fly • Some pets are cats • Whiskers is a cat Which statement must be true?
This requires multi-step logical deduction:
• Every cat is a mammal
• No mammal can fly
• Some pets are cats
• Whiskers is a cat

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Whiskers cannot fly

Question 7

Given these logical premises: • All A are B • No B are C • All D are A • Some E are D Which statement must be true?
This requires multi-step logical deduction:
• All A are B
• No B are C
• All D are A
• Some E are D

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Some E are not C

Question 8

Given these logical premises: • If P, then Q • If Q, then R • If R, then S • Not S Which statement must be true?
This requires multi-step logical deduction:
• If P, then Q
• If Q, then R
• If R, then S
• Not S

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Not P

Question 9

Given these logical premises: • If it's Monday, then school is open • If school is open, then buses run • Buses are not running Which statement must be true?
This requires multi-step logical deduction:
• If it's Monday, then school is open
• If school is open, then buses run
• Buses are not running

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: It's not Monday

Question 10

Given these logical premises: • Either John or Mary broke the vase • If John broke it, he would admit it • John didn't admit it Which statement must be true?
This requires multi-step logical deduction:
• Either John or Mary broke the vase
• If John broke it, he would admit it
• John didn't admit it

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Mary broke the vase

Question 11

Given these logical premises: • All X are Y • Some Y are Z • No Z are W • P is X Which statement must be true?
This requires multi-step logical deduction:
• All X are Y
• Some Y are Z
• No Z are W
• P is X

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: P is not W

Question 12

Given these logical premises: • Every cat is a mammal • No mammal can fly • Some pets are cats • Whiskers is a cat Which statement must be true?
This requires multi-step logical deduction:
• Every cat is a mammal
• No mammal can fly
• Some pets are cats
• Whiskers is a cat

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Whiskers cannot fly

Question 13

Given these logical premises: • If A, then B • If B, then C • If C, then not D • A is true Which statement must be true?
This requires multi-step logical deduction:
• If A, then B
• If B, then C
• If C, then not D
• A is true

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: D is false

Question 14

Given these logical premises: • If P, then Q • If Q, then R • If R, then S • Not S Which statement must be true?
This requires multi-step logical deduction:
• If P, then Q
• If Q, then R
• If R, then S
• Not S

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Not P

Question 15

Given these logical premises: • All A are B • No B are C • All D are A • Some E are D Which statement must be true?
This requires multi-step logical deduction:
• All A are B
• No B are C
• All D are A
• Some E are D

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Some E are not C

Question 16

Given these logical premises: • The light is either on or off • If the light is on, the switch is up • The switch is not up Which statement must be true?
This requires multi-step logical deduction:
• The light is either on or off
• If the light is on, the switch is up
• The switch is not up

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: The light is off

Question 17

Given these logical premises: • If it's a weekday, I work • If I work, I get tired • If I'm tired, I sleep early • I didn't sleep early Which statement must be true?
This requires multi-step logical deduction:
• If it's a weekday, I work
• If I work, I get tired
• If I'm tired, I sleep early
• I didn't sleep early

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: It's not a weekday

Question 18

Given these logical premises: • The light is either on or off • If the light is on, the switch is up • The switch is not up Which statement must be true?
This requires multi-step logical deduction:
• The light is either on or off
• If the light is on, the switch is up
• The switch is not up

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: The light is off

Question 19

Given these logical premises: • Either John or Mary broke the vase • If John broke it, he would admit it • John didn't admit it Which statement must be true?
This requires multi-step logical deduction:
• Either John or Mary broke the vase
• If John broke it, he would admit it
• John didn't admit it

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Mary broke the vase

Question 20

Given these logical premises: • Every cat is a mammal • No mammal can fly • Some pets are cats • Whiskers is a cat Which statement must be true?
This requires multi-step logical deduction:
• Every cat is a mammal
• No mammal can fly
• Some pets are cats
• Whiskers is a cat

Applying logical rules (modus ponens, modus tollens, contrapositive, transitive property, quantifier logic), we can conclude: Whiskers cannot fly
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