Either-Or Logic
Either-Or Logic problems present two conclusions that are complementary - exactly one of them must be true based on the given statements. Common complementary pairs include (A > C, A ≤ C), (A < C, A ≥ C), (A = C, A ≠ C). These problems test your ability to recognize when two conclusions together cover all possible scenarios.
What You'll Learn
Introduction to Either-Or Logic
Either-Or Logic problems present two conclusions that are complementary - exactly one of them must be true based on the given statements. Common complementary pairs include (A > C, A ≤ C), (A < C, A ≥ C), (A = C, A ≠ C). These problems test your ability to recognize when two conclusions together cover all possible scenarios.
Prerequisites
How to Solve Either-Or Logic Problems
Step 1: Decode the given inequality statement(s)
Step 2: Identify the relationship between the variables in the conclusions
Step 3: Check if the two conclusions are complementary (they cover all possibilities)
Step 4: Common complementary pairs: (>, ≤), (<, ≥), (=, ≠), (≥, <), (≤, >)
Step 5: Determine if the given information forces one of them to be true
Step 6: If the information allows both to be false or both to be true, 'Either-Or' does NOT follow
Step 7: If exactly one must be true in all possible scenarios, 'Either-Or' follows
Step 8: Answer accordingly
Example Problem
Example: Statement: A > B < C. Conclusions: I. A > C, II. A ≤ C. Which is true? Solution: Step 1: Decode: A > B < C Step 2: A and C have no definite relationship (signs are opposite) Step 3: Possible relationships between A and C: A > C, A = C, or A < C Step 4: Conclusion I (A > C) could be true but not necessarily Step 5: Conclusion II (A ≤ C) means A < C OR A = C Step 6: Together, I and II cover all possibilities (either A > C OR A ≤ C) Step 7: Since A and C must have SOME relationship, exactly one of I or II is true Answer: Either I or II follows
Pro Tips & Tricks
- Complementary pairs: (A > C, A ≤ C), (A < C, A ≥ C), (A = C, A ≠ C)
- (A ≥ C, A < C) and (A ≤ C, A > C) are also complementary
- When no definite relationship exists between variables, complementary pairs often follow
- If a definite relationship exists (e.g., A > C is certain), then 'Either-Or' does not apply (only I follows)
- Both conclusions cannot be false simultaneously if they are complementary
- Both conclusions can be true only if the relationship is both > and ≤ (impossible)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Either-Or Logic. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Either-Or Logic is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Either-Or Logic?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: