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Verification of Truth of the Statement

Reasoning · Logical & Analytical Reasoning

7 Part2 worked examples4 practice questions

“Is this true?” — the question is asked in different ways. One: is something true of a thing in every case or only sometimes? (“What does a pen always have?”) Two: some facts are given; on those facts is this statement true, false or can nothing be said? Three: some people speak about each other; who is telling the truth?

One habit serves in all three: do not take “often” for “always”, and do not take “may be” for “is”. What holds true in every possible situation is the one that is certainly true.

How to use this chapter

  1. Read — each part gives the idea, tables and a test.
  2. Study the solved example — beside each option the reason is open.
  3. Try it yourself — apply the test first, then pick the option.
  4. Know the level — Basic, Standard, Advanced.
NoteThe questions you solve are remembered in this browser; see your progress on the right (the “Contents” button on a phone).
1

Foundation — always versus often

Spotting the essential feature

The test for “always has”, four slips and a map of the whole chapter.

Map of the chapter — three checks of truth

Always true · true on the facts · who speaks truth

The three kinds of question, their answer options and the single test behind them.

TypeWhat it looks likeHow the answer comes
1. The essential feature“A pen always has — (a) cap (b) ink …”Remove it: is the thing still the same thing?
2. Facts → statement“Facts: A is taller than B … Statement: C is taller than A — true / false / cannot be said?”Try every possible situation: true in all = true; false in all = false; true in some, false in others = cannot be said
3. Truth-tellers“A says: B is lying … who tells the truth?”Try all the possibilities; the one that fits every statement is the answer

The idea is one in all three: “certain” is what stands in every possibility. In the first type the possibilities are all the forms of a pen; in the second all the situations that fit the facts; in the third all the splits of who tells truth and who lies.

The plain way for every question
List the possibilitiesTest the statement on eachTrue in all / false in all / mixedPick the answer

“Always has” — the test of the essential feature

Take it away and see

The difference between essential and usual features, the “remove-and-see” test and first examples.

A thing has many features. Some are such that without them it stops being that thing — these are essential. Others are common, some are found only in some kinds, and some are matters connected with it or its results. If the question says “always”, the answer is only the essential feature.

The “remove-and-see” test
Take the option awayAsk: is it still the same thing?Yes → not essentialNo → essential

Example: remove the cap of a pen — it is still a pen. Remove the clip — still a pen. But remove the ink and it will not write; it is no pen, only an empty tube. So the “always” answer is ink.

NoteSeveral features of the same thing may seem “right” (a pen often has a cap). The question’s word is “always” or “must”, not “often” or “usually” — so set aside those that may be missing.
Example 1 · Basic
pen — choose the feature that every pen must have (without it, it would not be a pen).
Solution, step by step
  1. 1The test: take the option away — would it still be called a pen? A pen writes only with ink; the cap, clip and body vary (metal or wood also).
  2. 2The other options: cap — usual, but without it the thing is still the same thing; clip — usual, but without it the thing is still the same thing; plastic body — found only in some kinds.
Answer ink
A pen remains after cap, clip and body are removed; not after the ink.
BasicTry it yourself first
candle — choose the feature that every candle must have (without it, it would not be a candle).
BasicTry it yourself first
bicycle — choose the feature that every bicycle must have (without it, it would not be a bicycle).

Four slips — how wrong options are made

Usual, in some, connected, result

The four moulds of wrong options and a way to recognise each.

SlipHow to recogniseExample
Usual but not essentialThe feeling that “every pen surely has some such thing”pen — cap; examination — exam hall
Only in some kindsFound in some forms, not alldesert — sand; camera — film
Connected but not a partSeen with it but no part of itkite — wind; camera — tripod
A result or a useComes after it or because of itfire — ash; examination — result
TrickThe biggest trap is the “usual” one, because it is so common that it begins to feel like “always”. Test it by thinking of one exception — a pen without a cap, a desert without sand, a camera without film. If an exception exists, the option is out.
Example 2 · Basic
examination — choose the feature that every examination must have (without it, it would not be a examination).
Solution, step by step
  1. 1The test: take the option away — would it still be called a examination? No examination without questions; result and certificate come after it, and an online exam has no hall.
  2. 2The other options: exam hall — usual, but without it the thing is still the same thing; certificate — this is a result or a use, not a part; result — this is a result or a use, not a part.
Answer questions
Result and certificate come after the exam; a hall is absent in an online exam; questions are always there.
BasicTry it yourself first
rain — choose the feature that every rain must have (without it, it would not be a rain).
BasicTry it yourself first
fire — choose the feature that every fire must have (without it, it would not be a fire).
2

“Always has” — practice by theme

Everyday things, places and events, nature and science

The essential features of forty things — apply the remove-and-see test in each question.

Everyday things

Shoe, newspaper, cupboard, kite, ladder, camera, mirror, magnet, compass

Essential and optional parts of household objects.

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Places, institutions and events

School, library, hospital, bank, market, field, well, bridge, museum, election, kitchen, week

Essential elements of places and institutions.

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Nature and science

River, lake, desert, island, forest, mountain, volcano, tree, diamond, shapes, leap year

The defining features of natural things and geometric shapes.

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3

Judging a statement from facts

True · false · cannot be said

Deciding the truth of a statement from chains of comparison and differences in age.

Facts of comparison

Height, weight, age, marks — join the links

The test of the three verdicts (true / false / open) and the way of joining links.

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Differences in age

Differences add up; an age needs an anchor

Checking statements from age-difference facts: with a chain the difference is fixed, with an anchor the age is fixed.

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Which of four statements is true

Only one is certainly true

Choosing the statement that is certainly true from four.

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4

Truth-tellers and liars

Try all the possibilities

People say things about one another; the split that fits every statement is the answer.

Who is telling the truth

Assume, check, strike off

The rule of the truth-liar puzzle, the six forms of statement and a table to test every split.

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How many liars, and is so-and-so truthful?

The same split, a different question

Giving the number of liars or one person’s type from the same solution.

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5

Strategy guide

One order for each type and the traps to avoid

The order of spotting and solving the three types and the common mistakes.

Spot the type, then pick the test

Three types, three tests

A table for spotting the type from the words of the question.

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Common traps and time-savers

The mistakes that keep happening

Reasons for losing marks in truth-checking questions.

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6

Mixed practice

All three types mixed

Questions on facts, age and truth-liars in three levels.

Basic practice

Direct chains, direct differences

Simple comparisons, ages and three-person truth-liar puzzles.

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Standard practice

Telling open from false

Cannot-be-said questions and longer chains.

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Advanced practice

Five persons, four speakers, long chains

Comparisons of five persons and four-person truth-liar puzzles.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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