Only Statement Pattern
Only Statement Pattern involves statements that use the word 'Only' (e.g., 'Only A are B'). This is logically equivalent to 'All B are A' (the reverse of what it might seem). Understanding this conversion is crucial for solving these problems correctly.
What You'll Learn
Introduction to Only Statement Pattern
Only Statement Pattern involves statements that use the word 'Only' (e.g., 'Only A are B'). This is logically equivalent to 'All B are A' (the reverse of what it might seem). Understanding this conversion is crucial for solving these problems correctly.
Prerequisites
How to Solve Only Statement Pattern Problems
Step 1: Identify any 'Only' statements in the premises
Step 2: Convert 'Only A are B' to 'All B are A'
Step 3: Convert 'Only A are not B' to 'All B are not A' or 'No B is A'
Step 4: Rewrite all statements in standard categorical form
Step 5: Apply standard syllogism rules to the converted statements
Step 6: Draw Venn diagrams if needed for verification
Step 7: Evaluate conclusions based on the converted statements
Example Problem
Example: Statements: Only citizens can vote. All voters are adults. Conclusions: I. All citizens are adults. II. Some adults are citizens. Solution: Step 1: 'Only citizens can vote' means only citizens are voters Step 2: Convert: 'Only citizens are voters' = 'All voters are citizens' Step 3: Second statement: 'All voters are adults' Step 4: We have: All voters are citizens; All voters are adults Step 5: From these, we cannot conclude 'All citizens are adults' (citizens may be larger than voters) → Conclusion I does NOT follow Step 6: We can conclude that some adults (the voters) are citizens → Conclusion II FOLLOWS Answer: Only conclusion II follows
Pro Tips & Tricks
- 'Only A are B' = 'All B are A' (not 'All A are B')
- 'Only A are B' means B is a subset of A
- 'Only A are B' can also be written as 'No non-A is B'
- Memorize: 'Only' reverses the relationship
- Example: 'Only students are toppers' = 'All toppers are students'
- Draw Venn diagram: put B inside A
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Only Statement Pattern. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Only Statement Pattern is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Only Statement Pattern?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: