Below is given a statement followed by some conclusions. Assuming statement to…
2023
Below is given a statement followed by some conclusions. Assuming statement to be universally true, decide which of the conclusions follow from the given statement. Statement: No cap is socks. Some caps are gloves. Conclusions: I. All gloves are socks. II. All socks are gloves. III. Some gloves are caps.
- A.
If only conclusion I follows
- B.
If only conclusion II follows
- C.
If only conclusion III follows
- D.
If none of the conclusions I, II, III follows
- E.
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Correct answer: C
To determine which conclusions follow, we can represent the given statements using a Venn diagram approach.
Statement Analysis
Statement 1: "No cap is socks."
This means the set of "caps" and the set of "socks" are entirely separate and do not overlap.
Statement 2: "Some caps are gloves."
This means there is an intersection between the set of "caps" and the set of "gloves."
Evaluating Conclusions
Conclusion I: "All gloves are socks."
This does not follow. The statements do not provide information establishing a relationship between all gloves and socks.
Conclusion II: "All socks are gloves."
This does not follow. There is no information in the statements that links all socks to gloves.
Conclusion III: "Some gloves are caps."
This follows directly from the second statement ("Some caps are gloves"). If some caps are gloves, then by definition, some gloves must also be caps.
Since only Conclusion III follows, Option 3 is the correct answer.
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