Statements:
All horses are donkeys. Some cats are monkeys. All monkeys are donkeys.
Conclusions:
(I) All cats are donkeys.
(II) Some horses are monkeys.
Analyzing Logical Statements and Conclusions
This solution analyzes the logical relationship between the given statements and conclusions to determine which conclusions logically follow.
Statement Analysis
- Statement 1: All horses are donkeys. This means the set of horses is a subset of the set of donkeys. (Mathematically: \( H \subseteq D \))
- Statement 2: Some cats are monkeys. This means there is at least one cat that is also a monkey. (Mathematically: \( C \cap M \neq \emptyset \))
- Statement 3: All monkeys are donkeys. This means the set of monkeys is a subset of the set of donkeys. (Mathematically: \( M \subseteq D \))
Conclusion Evaluation
Evaluating Conclusion (I): All cats are donkeys
- From Statement 2 (\( C \cap M \neq \emptyset \)) and Statement 3 (\( M \subseteq D \)), we can infer that the cats which are monkeys must also be donkeys. Thus, some cats are donkeys (\( C \cap D \neq \emptyset \)).
- However, the statements do not provide any information about cats that are *not* monkeys. We cannot conclude that these cats are also donkeys.
- Therefore, the conclusion All cats are donkeys (\( C \subseteq D \)) does not necessarily follow.
Evaluating Conclusion (II): Some horses are monkeys
- Statement 1 establishes \( H \subseteq D \).
- Statement 3 establishes \( M \subseteq D \).
- Both horses and monkeys are contained within the larger category of donkeys. However, the statements do not indicate any overlap or direct relationship between the set of horses and the set of monkeys.
- It is possible for the sets of horses and monkeys to be entirely separate within the set of donkeys.
- Therefore, the conclusion Some horses are monkeys (\( H \cap M \neq \emptyset \)) does not necessarily follow.
Final Determination
Based on the analysis, neither Conclusion (I) nor Conclusion (II) is logically guaranteed by the given statements. Both conclusions are possible but not certain.
Thus, the correct option is that Neither conclusion (I) nor (II) follows.
Important Questions from Syllogism (Notes)
Which conclusion would follow the given statements.
Statement:
Some Apples are Banana.
Some bananas are Grapes.
No Grape is Book.
Conclusion:
(I) Some Apples are Book is a possibility.
(II) All Bananas are Book.
In light of the above statements, choose the most appropriate answer from the options given below.- Disregard commonly known facts. Which conclusion would follow on the basis of given statements only.
Statement: Some bottles are car. some cars are cycle.
Conclusion:
(I) Some bottles are cycle is a possibility
(II) All bottles are cycle
In light of the above statements, choose the most appropriate answer from the options given below. - Statements :
All books are cakes.
All cakes are apples.
Conclusions:
I. Some cakes are books
II. No cake is books
III. Some apple are books
IV. All apples are books
Choose the correct option: - All household pets are domestic animals. NO unicorns are domestic animals. Therefore some Unicorns are not household pets. Which type of formal fallacy committed in the above argument ?
- Statements:
Some bags are purses. All purses are containers all containers are suitcases.
Conclusions :
I. Some suitcases are bags
II. All purses are bags
III. All Purses are suitcases
(IV) Some containers are purses
