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Basic Disjunction (OR)

Basic Disjunction (OR) problems involve the logical operator ∨ (OR), which produces a true output when at least one of the input propositions is true. The inclusive OR (standard in logic) is true even when both are true. These problems test your understanding of the 'at least one' rule.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Basic Disjunction (OR)

Basic Disjunction (OR) problems involve the logical operator ∨ (OR), which produces a true output when at least one of the input propositions is true. The inclusive OR (standard in logic) is true even when both are true. These problems test your understanding of the 'at least one' rule.

Prerequisites

Understanding of true/false values Basic propositional logic Truth table concepts OR operator definition
Why This Matters: Disjunction is a fundamental logical connective. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Basic Disjunction (OR) Problems

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Step 1: Identify the two propositions (p and q) being connected by OR

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Step 2: Recall that p ∨ q is TRUE when AT LEAST ONE of p or q is true

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Step 3: For truth table problems, evaluate all four possible combinations

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Step 4: The result is false only when both propositions are false

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Step 5: For word problems, check if at least one condition is satisfied

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Step 6: Verify your answer against the truth table

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Step 7: Present the truth value or conclusion

Pro Strategy: Check if either condition is true. If at least one is true, the disjunction is true. The only false case is when both are false.

Example Problem

Example: If p = 'It is raining' (False) and q = 'The ground is wet' (True), what is p ∨ q? Solution: Step 1: p = False, q = True Step 2: At least one is true (q is true) Step 3: p ∨ q = True Answer: True

Pro Tips & Tricks

  • p ∨ q is false only when p is false AND q is false
  • Three combinations yield true out of four possibilities
  • Inclusive OR includes the case where both are true
  • The ∨ symbol is often read as 'or'
  • Disjunction is commutative: p ∨ q ≡ q ∨ p
  • Disjunction is associative: (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Shortcut Methods to Solve Faster

T ∨ T = T
T ∨ F = T
F ∨ T = T
F ∨ F = F
p ∨ p ≡ p (idempotent law)

Common Mistakes to Avoid

Thinking OR is false when both are true (confusing with XOR)
Forgetting that OR is true when at least one is true
Confusing inclusive OR with exclusive OR
Misinterpreting 'either...or' in word problems

Exam Importance

Basic Disjunction (OR) is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
GMAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Basic Disjunction (OR)?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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