In this question, three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All phones are TVs. Some TVs are big. Some big are cars. Conclusions: I.Some TVs are phones. II.Some big are TVs. III.All big are cars.

Correct — B. Two of these three conclusions are simple conversions of the statements themselves.

Rule: 'All A are B' converts to 'Some B are A', and 'Some A are B' converts to 'Some B are A'.

I. All phones are TVs, so some TVs are phones. I follows.

II. Some TVs are big converts straight into some big are TVs. II follows.

III. The premise offers only 'Some big are cars'. It gives no ground at all for 'All big are cars', so III fails.

I and II follow — option (b).

Why the others are wrong

• (a)
  Only conclusions II and III follow. — II is fine, but III upgrades 'some' into 'all'. 'Some big are cars' leaves open a big thing that is not a car, so the universal cannot be drawn.
• (c)
  None of the conclusions follows. — Both I and II are straight conversions. 'All phones are TVs' guarantees some TVs are phones, and 'Some TVs are big' guarantees some big are TVs.
• (d)
  Only conclusion III follows. — III is the single conclusion that fails here. A particular premise never yields a universal conclusion, while the two conversions this option rejects are both valid.

This three-statement syllogism turns on two conversion rules and nothing else.

A universal affirmative converts partially. 'All phones are TVs' gives 'Some TVs are phones', because phones exist and each of them is a TV. It does not give 'All TVs are phones'.

A particular affirmative converts fully. 'Some TVs are big' and 'Some big are TVs' say the same thing, so one is available the instant the other is stated.

What can never be done is strengthening a quantifier. 'Some big are cars' does not become 'All big are cars', however the classes are drawn.

Key facts

• 'All A are B' yields 'Some B are A' under the exam's non-empty class convention.
• 'Some A are B' and 'Some B are A' are equivalent statements.
• A particular premise never supports a universal conclusion.
• 'Some big are cars' leaves open the existence of a big thing that is not a car.

Common traps

• Rejecting I because 'All phones are TVs' feels one-directional.
• Reading 'Some big are cars' as though the sample covered the whole class.
• Choosing 'None follows' when two conclusions are restatements of the premises.

No directly related past PYQ was found.