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Tautology and Contradiction - Absolute-Beginner Level: core concept mastery Tautology and Contradiction ABSOLUTE BEGINNER

This skill primer 🌟 worksheet focuses on Tautology and Contradiction - a key topic in Logical Connectives. You'll solve 20 absolute-beginner-level problems (Worksheet 1 of 10). The primary focus is on core concept mastery. Master tautology and contradiction problems, tautology and contradiction reasoning questions, and tautology and contradiction practice through systematic practice.

📝 Worksheet 1 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Absolute Beginner level

What you'll learn in this worksheet:
Your progress through Tautology and Contradiction
Worksheet 1 of 10 (0% complete)

Question 1

Classify the following logical statement: (p → q) → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) → p

Step 3: Test all possible combinations
This is contingent - depends on values of p and q

Question 2

Classify the following logical statement: (p → q) ∨ (¬p → q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) ∨ (¬p → q)

Step 3: Test all possible combinations
This simplifies to q ∨ ¬q, which is always True

Question 3

Classify the following logical statement: (p → q) → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) → p

Step 3: Test all possible combinations
This is contingent - depends on values of p and q

Question 4

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false

Question 5

Classify the following logical statement: (p → q) → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) → p

Step 3: Test all possible combinations
This is contingent - depends on values of p and q

Question 6

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false

Question 7

Classify the following logical statement: p ∧ ¬p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p ∧ ¬p

Step 3: Test all possible combinations
Truth table:
p=T: T ∧ F = F
p=F: F ∧ T = F
Result: Always False → CONTRADICTION
This violates the Law of Non-Contradiction

Question 8

Classify the following logical statement: (p → q) → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) → p

Step 3: Test all possible combinations
This is contingent - depends on values of p and q

Question 9

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false

Question 10

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false

Question 11

Classify the following logical statement: p → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p → p

Step 3: Test all possible combinations
Truth table:
p=T: T → T = T
p=F: F → F = T
Result: Always True → TAUTOLOGY
This is the Law of Identity

Question 12

Classify the following logical statement: p ∨ ¬p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p ∨ ¬p

Step 3: Test all possible combinations
Truth table:
p=T: T ∨ F = T
p=F: F ∨ T = T
Result: Always True → TAUTOLOGY
This is the Law of Excluded Middle

Question 13

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false

Question 14

Classify the following logical statement: p → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p → p

Step 3: Test all possible combinations
Truth table:
p=T: T → T = T
p=F: F → F = T
Result: Always True → TAUTOLOGY
This is the Law of Identity

Question 15

Classify the following logical statement: (p → q) ∨ (¬p → q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) ∨ (¬p → q)

Step 3: Test all possible combinations
This simplifies to q ∨ ¬q, which is always True

Question 16

Classify the following logical statement: p ∧ ¬p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p ∧ ¬p

Step 3: Test all possible combinations
Truth table:
p=T: T ∧ F = F
p=F: F ∧ T = F
Result: Always False → CONTRADICTION
This violates the Law of Non-Contradiction

Question 17

Classify the following logical statement: p → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p → p

Step 3: Test all possible combinations
Truth table:
p=T: T → T = T
p=F: F → F = T
Result: Always True → TAUTOLOGY
This is the Law of Identity

Question 18

Classify the following logical statement: (p → q) → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p → q) → p

Step 3: Test all possible combinations
This is contingent - depends on values of p and q

Question 19

Classify the following logical statement: p → p Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: p → p

Step 3: Test all possible combinations
Truth table:
p=T: T → T = T
p=F: F → F = T
Result: Always True → TAUTOLOGY
This is the Law of Identity

Question 20

Classify the following logical statement: (p ∧ q) ∧ ¬(p ∧ q) Is it a Tautology (always True), Contradiction (always False), or Contingent (depends on variables)?
Step 1: Understand the classifications
• Tautology: Always True for all possible truth values
• Contradiction: Always False for all possible truth values
• Contingent: True for some values, False for others

Step 2: Analyze the expression
Expression: (p ∧ q) ∧ ¬(p ∧ q)

Step 3: Test all possible combinations
A statement cannot be both true and false
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