Statements:
Some cows are goats.
Some goats are dogs.
All dogs are tigers.
Conclusions:
(I) All dogs are cows.
(II) Some tigers are goats.
To solve this logical reasoning problem, we need to analyze the given statements and determine which conclusions necessarily follow from them.
Analyzing the Statements
- Statement 1: Some cows are goats. (This means there is at least one cow that is also a goat, indicating an overlap between the sets 'cows' and 'goats'.) Symbolically, $C \cap G \neq \emptyset$.
- Statement 2: Some goats are dogs. (This means there is at least one goat that is also a dog, indicating an overlap between the sets 'goats' and 'dogs'.) Symbolically, $G \cap D \neq \emptyset$.
- Statement 3: All dogs are tigers. (This means the entire set 'dogs' is contained within the set 'tigers'.) Symbolically, $D \subseteq T$.
Evaluating Conclusion (I)
Conclusion (I): All dogs are cows.
- We know from Statement 2 that some goats are dogs ($G \cap D \neq \emptyset$).
- We know from Statement 1 that some cows are goats ($C \cap G \neq \emptyset$).
- However, the relationship between cows and dogs is not directly established, and the overlaps mentioned ('some') do not guarantee that the entire set of dogs is included within the set of cows ($D \subseteq C$). It's possible for the dogs that are goats to be completely separate from the cows that are goats.
- Therefore, Conclusion (I) does not logically follow.
Evaluating Conclusion (II)
Conclusion (II): Some tigers are goats.
- From Statement 2, we know that there exist individuals that are both goats and dogs ($G \cap D \neq \emptyset$).
- From Statement 3, we know that every dog is also a tiger ($D \subseteq T$).
- Combining these, the individuals that are both goats and dogs must also be tigers. This implies that there must be an overlap between the set of tigers and the set of goats. Symbolically, since $G \cap D \neq \emptyset$ and $D \subseteq T$, it follows that $(G \cap D) \subseteq (G \cap T)$, meaning $G \cap T \neq \emptyset$.
- Therefore, Conclusion (II) logically follows.
Final Determination
Based on the analysis, only Conclusion (II) is logically derived from the given statements.
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
