Three statements are given followed by four conclusions I, II, III and IV. You…
2020
Three statements are given followed by four conclusions I, II, III and IV. You have to consider these statements to be true, even if they seem at variance from commonly known facts. Decide which of the given conclusions logically follow/s from the given statement.
Statements:
A. All beetroots are carrots.
B. All carrots are radishes.
C. All radishes are white.
Conclusions:
I. All beetroots are white.
II. All white are carrots.
III. All radishes are beetroots.
IV. All carrots are white.
- A.
Only conclusions II and III follow.
- B.
All the conclusions follow.
- C.
Only conclusions I and IV follow.
- D.
Only conclusions I and II follow.
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Treat each statement as true and arrange them as a single chain of subsets:
All beetroots are carrots → Beetroots ⊆ Carrots.
All carrots are radishes → Carrots ⊆ Radishes.
All radishes are white → Radishes ⊆ White.
Combining: Beetroots ⊆ Carrots ⊆ Radishes ⊆ White.
Now test each conclusion:
I. All beetroots are white — beetroots lie inside white through the chain → FOLLOWS.
II. All white are carrots — this is the converse of 'all carrots are white'; the chain does not guarantee a converse, so 'white' need not lie inside carrots → does NOT follow.
III. All radishes are beetroots — this is the converse of 'all beetroots are radishes'; the statements establish only that beetroots are radishes, not the reverse, so it is not guaranteed → does NOT follow.
IV. All carrots are white — carrots lie inside white through the chain → FOLLOWS.
Therefore only conclusions I and IV follow, which matches the option 'Only conclusions I and IV follow.'