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Statements: 1. Some hens are cows 2. A...

Statements: 1. Some hens are cows
2. All cows are horses
Conclusions: 1. Some horses are hens
2. Some hens are horses

A

only conclusion 1 follows,

B

only conclusion 2 follows,

C

either conclusion 1 or 2 follows,

D

both conclusion 1 and 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: "Some hens are cows." This means there is at least one hen that is also a cow. - Statement 2: "All cows are horses." This means every cow is also a horse. 2. **Visual Representation**: - We can represent this using Venn diagrams: - Draw a circle for hens (H). - Draw a circle for cows (C) that overlaps with the hens circle, indicating that some hens are cows. - Draw a larger circle for horses (H) that completely encompasses the cows circle, indicating that all cows are horses. 3. **Analyzing the Conclusions**: - Conclusion 1: "Some horses are hens." - Since some hens are cows and all cows are horses, it follows that those hens that are cows must also be horses. Therefore, this conclusion is valid. - Conclusion 2: "Some hens are horses." - Since we established that some hens are cows and all cows are horses, it follows that those hens that are cows are also horses. Therefore, this conclusion is also valid. 4. **Final Decision**: - Both conclusions are valid based on the statements provided. Thus, the answer is that both conclusions follow from the statements. ### Final Answer: Both conclusion 1 and conclusion 2 follow from the statements.
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MCGROW HILL PUBLICATION-ADDITIONAL TOPICS IN MENTAL MATH-EXERCISE 2
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