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: No card is a parcel. All cards are envelopes. Some envelopes are bags. Conclusions: I. All envelopes can never be parcels. II. No card is a bag. III. At least some bags are postcards.

Correct — A. Test each conclusion against the three statements alone, ignoring what you know about the world.

I follows. All cards are envelopes, and no card is a parcel. So every card is an envelope that is not a parcel — which makes 'all envelopes are parcels' impossible, and that is exactly what I claims.

II does not follow. Some envelopes are bags, and all cards are envelopes, so those bag-envelopes could be the cards. 'No card is a bag' is possible, not certain.

III does not follow. The statements never mention postcards, so no conclusion about postcards can be drawn.

One conclusion is forced and two are not → option (a)

Why the others are wrong

• (b)
  Only II follows — II is a possibility, not a certainty. Cards are envelopes and some envelopes are bags, so a card is allowed to be a bag; nothing in the statements forbids it.
• (c)
  Only I and III follow — This option carries III, and III introduces postcards, a term that appears in no statement. A conclusion may not add a new term.
• (d)
  Only II and III follow — This option needs both of the failing conclusions: II is only a possibility and III rests on postcards, which the statements never mention.

A syllogism conclusion follows only if it is true in every arrangement the statements allow. One counter-arrangement is enough to reject it.

Draw the definite relations first. 'All cards are envelopes' puts the card circle inside the envelope circle; 'no card is a parcel' keeps parcels clear of that inner circle.

'Some envelopes are bags' is the loose premise. It fixes an overlap somewhere in the envelope circle but not where, so it can be drawn touching the cards or clear of them.

Key facts

• A conclusion follows only if it holds in every diagram consistent with the statements.
• 'All X can never be Y' is proved as soon as one X is known not to be a Y.
• A term appearing in a conclusion but in no statement, such as postcards, can never follow.
• 'Some A are B' never fixes where the overlap sits inside A.

Common traps

• Reading 'postcards' as a shorthand for 'cards'
• Treating 'some envelopes are bags' as if it excluded the cards
• Accepting II because it feels consistent with the statements rather than forced by them

No directly related past PYQ was found.