Inequalities

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Inequalities — Logical Reasoning Questions & Formulas

Logical Reasoning

5 questions

Evaluate a chain such as $P > Q \ge R = S$ . The highest-priority sign between two letters decides the result.

Priority	Signs	Rule
1 · King	$>$ , $<$	Overrides everything
2 · Soldier	$\ge$ , $\le$	Beats $=$ , loses to $>$ , $<$
3 · Public	$=$	Ignored unless it is the only sign

Gate-closed (broken chain): opposite-facing signs between two elements → no relation; any single definite conclusion is then False.
Either / Or applies only when the two conclusions use the same pair, both are individually false, and together they cover the split — e.g. I. $A > B$ , II. $A \le B$ ; or a Soldier split I. $A > B$ , II. $A =$ .

Flip the sign when multiplying / dividing by a negative, or taking reciprocals of same-sign values: $-x > 5 \Rightarrow x < -5$ ; $x > y \Rightarrow \frac1x < \frac1y$ .

B

A = B