Coded Inequalities
intermediate24 min read
Symbols stand in for the relations greater-than, less-than, equal, at-least and at-most. How to decode the symbols, build one combined chain, test each conclusion for a definite result, and spot the either-or complementary pair.
What you will be able to do
- Replace each coded symbol with its plain relation before doing anything else.
- Join the statements into a single chain and read the relation between two letters off it.
- Decide whether a conclusion is definitely true, not just possibly true.
- Recognise the either-or case: two conclusions that are individually uncertain but together exhaustive.
What is inside this lesson
- 1What the question gives you
- 2Decode, then build one chain
- 3Definite, not merely possible
- 4The either-or case
- 5Worked examples
- 6Common mistakes
- 7Quick revision
- 8Practice
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What the question gives you
A key defines symbols in terms of relations, for example:
P @ Qmeans P is not smaller than Q (so P ≥ Q)P & Qmeans P is not greater than Q (so P ≤ Q)P # Qmeans P is neither smaller than nor equal to Q (so P > Q)P © Qmeans P is neither greater than nor smaller than Q (so P = Q)P % Qmeans P is neither greater than nor equal to Q (so P < Q)
Then you get two or three coded statements and two or three coded conclusions, and you decide which conclusions definitely follow.
The lesson itself is for members
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