This is also known as the 'No Relation' rule. If you see signs like '>' and '<' appearing between two variables, you cannot determine a relationship. The path is closed. Any conclusion given for these variables will be false unless it covers all three possibilities (Greater, Smaller, and Equal). Example: In A > B < C, the conclusion A > C is false.

This case applies when two conclusions are individually false but logically cover all ground. Condition 1: Both elements in the conclusions must be the same. Condition 2: Both conclusions must be false. Condition 3: They must combine to match the statement. Example: If statement is A ≥ B, then 'Conclusion I: A > B' and 'Conclusion II: A = B' together form an Either-Or case.

Question Type Overview

Coded Inequality questions are a staple in SSC CGL, testing your ability to quickly interpret and deduce relationships. Instead of standard inequality symbols (>, <, =, ≥, ≤), you'll encounter arbitrary codes (e.g., @, #, $, %, &). Your task is to decode these symbols, combine statements, and identify which given conclusions are definitely true based on the established relationships. This section is a high-scoring opportunity, requiring sharp observation and logical deduction rather than complex calculations.

Pattern Recognition Rules

• Symbol Mapping: The most critical first step is to accurately map each given code to its corresponding standard inequality symbol. This mapping remains consistent for all questions in a set. Example: 'P @ Q' means 'P is greater than Q' (P > Q).
• Strong vs. Weak Symbols: Identify 'strong' symbols (>, <) and 'weak' symbols (≥, ≤). The presence of a strong symbol in a continuous path between two variables usually dictates the final relationship's strength.
• Opposite Gates: If, while tracing a path between two variables, you encounter symbols that open in opposite directions (e.g., A > B < C), no definite conclusion can be drawn between those variables (A and C in this case).
• Equality's Role: The '=' symbol acts as a neutral connector. It allows the flow of comparison but doesn't alter the direction or strength of the relationship.

Step-by-Step Approach

1. Decode the Symbols: At the start of the section, quickly jot down the symbol-to-sign mapping on your rough sheet. For example:
   • @ → >

   • → <

   • $ → =
   • % → ≥
   • & → ≤
2. Formulate the Statement Chain: Mentally (or on rough paper for complex cases) combine the given statements into a single, continuous chain, substituting the codes with their actual symbols. Ensure variables are linked correctly. Example: Statement: A % B, B @ C, C $ D. Decoded: A ≥ B > C = D.
3. Analyze Each Conclusion: For each conclusion (e.g., A @ D, meaning A > D), identify the two variables involved and trace the path between them in your decoded chain.
4. Apply the Gate Method: Imagine each symbol as a gate. You can only move through a gate if it's 'open' in the direction you're traveling. All gates in the path must open in the same direction for a definite conclusion.
   • Direction Check: If gates face opposite directions (e.g., A > B < C), stop immediately; no definite conclusion can be drawn.
   • Strength Check: If all gates face the same direction:
     • If any strong symbol (>, <) is present in the path, the conclusion must be strong (e.g., A > D if the path is A ≥ B > C = D).
     • If only weak symbols (≥, ≤) and/or '=' are present, the conclusion must be weak (e.g., A ≥ C if the path is A ≥ B ≥ C).

Time-Saving Shortcut

• Mental Mapping & Tracing: Avoid writing out the full decoded chain for every question. Practice mentally decoding symbols and tracing the path between the conclusion's variables directly from the coded statement.
• First Glance for Opposites: When checking a conclusion, quickly scan the path between the two variables for any opposing symbols. If found, mark 'False' or 'Cannot be determined' instantly.
• Strongest Link Rule: If all gates align, quickly identify if there's a strong symbol (>, <) in the path. If yes, the conclusion must be strong. If only weak symbols (≥, ≤) or '=' are present, the conclusion must be weak. This saves time on detailed symbol evaluation.

Question Type Overview

Mathematical Inequality questions in SSC CGL primarily test your ability to establish relationships between variables based on given statements. You'll encounter two main types:

1. Direct Inequalities: Statements are given using standard symbols (>, <, =, ≥, ≤). E.g., A > B ≥ C.
2. Coded Inequalities: Symbols are replaced by codes (e.g., 'P @ Q' means 'P is greater than Q'). You first decode the symbols and then solve as direct inequalities.

Pattern Recognition Rules

To solve quickly, internalize these rules:

• The 'Gate' Method: Imagine each symbol as a gate. > and ≥ are gates open from left to right. < and ≤ are gates open from right to left. = is open in both directions.
• Path Tracing: To establish a relation between two variables (e.g., X and Y), you must be able to travel from X to Y (or Y to X) through continuously 'open' gates.
• Opposite Gates = Blocked Path: If you encounter gates facing opposite directions in a path (e.g., A > B < C), the path is blocked, and no definite relationship can be established between the variables at the ends (A and C).
• Symbol Priority: When tracing a valid path, the conclusion's symbol is determined by priority:
  1. If > or < is present in the path, and all gates are open in one direction, this symbol takes highest priority. (e.g., A > B ≥ C implies A > C)
  2. If only ≥ or ≤ and = are present, then ≥ or ≤ takes priority. (e.g., A ≥ B = C implies A ≥ C)
  3. If only = is present, then = is the conclusion. (e.g., A = B = C implies A = C)

Step-by-Step Approach

Let's take an example: Statement: P > Q ≥ R = S < T. Conclusions: I. P > S II. Q = T

1. Identify Variables: For each conclusion, identify the two variables whose relationship needs to be checked.
   • For I: P and S.
   • For II: Q and T.
2. Trace the Path: Locate the variables in the statement and trace the path between them.
   • For I: P > Q ≥ R = S
   • For II: Q ≥ R = S < T
3. Check Gate Direction: Ensure all gates in the path are open in a single, consistent direction.
   • For I: P > Q ≥ R = S. All gates open from P towards S. Path is valid.
   • For II: Q ≥ R = S < T. The S < T gate faces opposite to Q ≥ R = S. Path is blocked.
4. Determine Dominant Symbol (if path valid):
   • For I: Path P > Q ≥ R = S contains >, ≥, =. The highest priority symbol is >. So, P > S is the definite conclusion. Conclusion I is TRUE.
   • For II: Path blocked. No definite conclusion. Conclusion II is FALSE.

Time-Saving Shortcut

• Visual Scan: For direct inequalities, quickly scan the path between variables. If you see opposing signs (e.g., > and < or ≥ and ≤ facing each other) between the two target variables, immediately mark 'no definite relation' for that pair without further analysis. This saves immense time.
• Mental Priority: As you scan a valid path, mentally note the strongest symbol encountered. If you see a > or <, that's your likely conclusion. If not, look for ≥ or ≤. If only =, then =. This mental hierarchy speeds up deduction.
• Combine Statements First: If multiple statements are given (e.g., A>B, B=C, C<D), mentally or quickly write them as a single chain (A>B=C<D) before checking conclusions.

When moving from one variable to another in a chain, the strongest symbol wins. If the chain contains '>', '≥', and '=', the result is always '>'. Think of '>' as a King, '≥' as a Prince, and '=' as a Soldier. The King always takes priority. Example: If P > Q ≥ R = S, then the conclusion P > S is true because the 'Greater than' sign exists in the path.