⚖️ Mathematical Inequality - Formula Sheet

🎯 Basic Symbols

Comparison Symbols

>  : Greater than
<  : Less than
≥  : Greater than or equal to
≤  : Less than or equal to
=  : Equal to
≠  : Not equal to

Coded Inequality Symbols

Common coding patterns:
@  → >
#  → <
$  → ≥
%  → ≤
&  → =
★  → ≠

📊 Solving Steps

Direct Inequality

1. Write mathematical expressions
2. Compare using given information
3. Find definite relationships
4. Answer based on conclusions

Coded Inequality

1. Decode symbols first
2. Write mathematical expressions
3. Solve step by step
4. Verify conclusions

🔢 Conclusion Types

Definite Conclusions

Only I follows
Only II follows
Both I and II follow
Neither I nor II follows
Either I or II follows

Either/Or Cases

When two conclusions are:
- Complementary (P > Q and P ≤ Q)
- Both cannot be false simultaneously
- Both cannot be true simultaneously

⚡ Common Patterns

Single Variable Comparisons

P > Q, Q > R → P > R
P > Q, Q = R → P > R
P = Q, Q > R → P > R

Multiple Variables

P > Q > R > S
A ≥ B ≥ C ≥ D
X = Y > Z = W

Combined Statements

P > Q, R < S, Q = R
Combine: P > Q = R < S

📝 Problem-Solving Strategy

Step-by-Step Method

1. Decode symbols (if coded)
2. Write all given statements
3. Combine related statements
4. Draw relationship diagrams
5. Check each conclusion
6. Mark valid/invalid conclusions

Quick Checking

Direct comparison: Check immediate relationships
Indirect comparison: Find common variables
Complex chains: Break into smaller parts

🔍 Common Question Types

Direct Questions

"Which conclusion definitely follows?"
"Which conclusion is possibly true?"

Coded Questions

"If @ means >, # means <, then..."
"Statements: P@Q#R, Conclusions: I. P>R II. Q>R"

Combined Conclusions

"Conclusions: I. P≥Q II. P=Q"
Check if either, both, or neither follow

⚡ Quick Tips

Symbol Priority

> and < are stronger than ≥ and ≤
= is definite, others are possibilities

Relationship Rules

If A > B and B > C, then A > C ✓
If A > B and B ≥ C, then A > C ✓
If A ≥ B and B > C, then A > C ✓

Common Mistakes to Avoid

Don't assume relationships not given
Don't confuse similar symbols
Check all possible paths
Consider equality cases separately

📚 Practice Approach

Daily Practice

1. Practice symbol decoding
2. Work on complex chains
3. Time yourself regularly
4. Review mistakes thoroughly

Speed Building

Memorize common codings
Practice mental combination
Learn to spot patterns quickly

Master Inequality - Decode, combine, conclude systematically! ⚖️