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Statements: 1. No magazine is cap. 2. ...

Statements: 1. No magazine is cap.
2. All caps are cameras
Conclusions: 1. No camera is magazine
2. Some cameras are magazines

A

only conclusion 1 follows,

B

only conclusion 2 follows,

C

either conclusion 1 or 2 follows,

D

neither conclusion 1 nor 2 follows,

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the given statements and conclusions logically. ### Step-by-Step Solution: 1. **Understanding the Statements:** - Statement 1: "No magazine is a cap." - This means that there is no overlap between the set of magazines (M) and the set of caps (C). We can represent this as: - M ∩ C = ∅ (the intersection of magazines and caps is empty) - Statement 2: "All caps are cameras." - This means that the entire set of caps is included in the set of cameras (K). We can represent this as: - C ⊆ K (caps are a subset of cameras) 2. **Visual Representation:** - Draw three circles: - Circle M for magazines. - Circle C for caps, which is entirely inside Circle K for cameras. - There is no intersection between Circle M and Circle C. 3. **Analyzing the Conclusions:** - Conclusion 1: "No camera is a magazine." - This conclusion suggests that the set of cameras (K) does not overlap with the set of magazines (M). - From our visual representation, we see that while there is no direct relationship stated between magazines and cameras, it is possible that some cameras could be magazines. Therefore, this conclusion is not necessarily true. - Conclusion 2: "Some cameras are magazines." - This conclusion states that there is at least some overlap between cameras (K) and magazines (M). - Given our visual representation, we see that there is no evidence to support this conclusion either, as the two sets are separate. 4. **Final Evaluation:** - Since the statements do not provide any direct relationship between magazines and cameras, we cannot definitively conclude either statement. - Thus, both conclusions cannot be true at the same time, and we find that: - Conclusion 1 is not necessarily true. - Conclusion 2 is also not necessarily true. ### Summary of Conclusions: - Conclusion 1: No camera is a magazine - **Not necessarily true.** - Conclusion 2: Some cameras are magazines - **Not necessarily true.**
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MCGROW HILL PUBLICATION-ADDITIONAL TOPICS IN MENTAL MATH-EXERCISE 2
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