Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. All coins are tokens.
2. No token is a stamp.
3. No stamp is a badge.
Conclusions:
I. Some coins are badges.
II. No coin is a badge.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Either conclusion I or conclusion II follows
When two conclusions do not follow on their own, but in every diagram exactly one of them is true (such as “some X are Y” and “no X is Y”), the answer is “either one or the other follows”.
“All coins are tokens”: the circle of coins lies inside the circle of tokens
“No token is a stamp”: the circles of tokens and stamps do not touch
“No stamp is a badge”: the circles of stamps and badges do not touch; nothing links the badges with the coins
Conclusion I: Some coins are badges. — Does not follow on its own. In case 2 the coins and badges do not meet, so it is false there.
Conclusion II: No coin is a badge. — Does not follow on its own. In case 1 some coins are badges, so it is false there.
Coins and badges either meet or they do not; there is no third case. So in every diagram exactly one of I and II is true: either conclusion I or conclusion II follows.