Given below are four statements. Among them two are related in such a way that…
2017
Given below are four statements. Among them two are related in such a way that they can both be true but they cannot both be false. Select the code that indicates those two statements :
Statements :
(a) Honest people never suffer.
(b) Almost all honest people do suffer.
(c) Honest people hardly suffer.
(d) Each and every honest person suffers.
Code :
Answer: D. (b) and (c) — Concept: the square of oppositionTraditional logic sorts every categorical statement about a subject class S and a predicate P into one of four forms: A —…
- A.
(a) and (b)
- B.
(a) and (c)
- C.
(a) and (d)
- D.
(b) and (c)
Show answer & explanation
Correct answer: D
Concept: the square of opposition
Traditional logic sorts every categorical statement about a subject class S and a predicate P into one of four forms:
A — universal affirmative: All S are P.
E — universal negative: No S is P.
I — particular affirmative: Some S are P.
O — particular negative: Some S are not P.
The square of opposition fixes how any two of these forms may vary in truth value:
Contradictories (A with O, and E with I): they always take opposite truth values, so they are never both true and never both false.
Contraries (A with E): two universals of opposite quality cannot both be true, but they can both be false.
Sub-contraries (I with O): two particulars of opposite quality can both be true, but they cannot both be false.
Subalternation (A with I, and E with O): the truth of the universal carries down to the particular, but truth does not travel back up.
So the property the question asks for — two statements that can both be true yet cannot both be false — is precisely the definition of a sub-contrary pair, and sub-contrariety holds between an I form and an O form.
Application: classify the four statements
Read every statement with S = honest people and P = suffer.
"Honest people never suffer" withholds suffering from every honest person: No S is P, the E form, a universal negative.
"Almost all honest people do suffer" ascribes suffering to some honest people, indeed to most of them: Some S are P, the I form, a particular affirmative.
"Honest people hardly suffer" says that most honest people escape suffering, that is, some honest people do not suffer: Some S are not P, the O form, a particular negative.
"Each and every honest person suffers" ascribes suffering to every honest person: All S are P, the A form, a universal affirmative.
A note on the wording: the traditional classification sorts a statement by the form its quantity word signals, not by an exact proportion. "Almost all honest people do suffer" affirms suffering of some honest people and therefore counts as the particular affirmative, while "Honest people hardly suffer" denies suffering of some honest people and therefore counts as the particular negative. Read instead as precise prevalence claims the two would sit awkwardly side by side, so keep the I and O reading that the traditional square uses — the reading behind the official CBSE UGC NET November 2017 Paper I key for this question.
Here the I form is ‘Almost all honest people do suffer’ and the O form is ‘Honest people hardly suffer’; those two statement values therefore make the sub-contrary pair that the code must indicate.
Cross-check: what the other pairings give
Statement pair | Forms | Relation and truth behaviour |
|---|---|---|
‘Honest people never suffer’ + ‘Almost all honest people do suffer’ | E and I | Contradictories — always opposite in truth value, so they are never both true and never both false. |
‘Honest people never suffer’ + ‘Honest people hardly suffer’ | E and O | Subalternation — the universal negative entails the particular negative; both can be true together and both can be false together. |
‘Honest people never suffer’ + ‘Each and every honest person suffers’ | E and A | Contraries — they cannot both be true, although both can be false together. |
‘Almost all honest people do suffer’ + ‘Honest people hardly suffer’ | I and O | Sub-contraries — they can both be true, and they cannot both be false. |
Read as those traditional forms, the two particular statements cannot both fail: their joint falsity would demand that no honest person suffers and that every honest person suffers at the same time, which is impossible, while a mixed population of honest people lets both statements hold at once. Therefore the code pairing ‘Almost all honest people do suffer’ with ‘Honest people hardly suffer’ is the required result.