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Statements: 1. All men are dogs 2. All...

Statements: 1. All men are dogs
2. All dogs are cats
Conclusions: 1. All men are cats
2. All cats are men

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. Here’s a step-by-step breakdown: ### Step 1: Understand the Statements 1. **Statement 1**: All men are dogs. 2. **Statement 2**: All dogs are cats. ### Step 2: Visualize with Venn Diagrams - Draw a Venn diagram with three circles: - Circle A for Men - Circle B for Dogs - Circle C for Cats ### Step 3: Place the Information in the Venn Diagram - Since "All men are dogs," Circle A (Men) is completely within Circle B (Dogs). - Since "All dogs are cats," Circle B (Dogs) is completely within Circle C (Cats). - Therefore, Circle A (Men) is also completely within Circle C (Cats). ### Step 4: Analyze the Conclusions 1. **Conclusion 1**: All men are cats. - Since all men are dogs and all dogs are cats, it follows that all men are also cats. This conclusion is **true**. 2. **Conclusion 2**: All cats are men. - This statement claims that every cat is a man. However, we know that there are cats that are not men (since there are dogs that are cats but not men). Therefore, this conclusion is **false**. ### Step 5: Final Decision - Based on the analysis: - Conclusion 1 is true. - Conclusion 2 is false. ### Summary of Results - Only Conclusion 1 follows from the statements provided.
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