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:
Analyzing the Logic Reasoning Statements
This problem involves logical deduction based on two initial statements and evaluating the validity of four possible conclusions.
Initial Statements
- Statement 1: All books are cakes.
- Statement 2: All cakes are apples.
Representing Statements Logically
We can represent these statements using set notation or logical quantifiers:
- Statement 1: Let B represent the set of 'books' and C represent the set of 'cakes'. The statement translates to $B \subseteq C$ (All elements in B are also in C).
- Statement 2: Let C represent the set of 'cakes' and A represent the set of 'apples'. The statement translates to $C \subseteq A$ (All elements in C are also in A).
Deriving Intermediate Conclusions
From the two statements, we can deduce a combined relationship:
Since all books are cakes ($B \subseteq C$) and all cakes are apples ($C \subseteq A$), it logically follows that all books are apples ($B \subseteq A$). This is a transitive property.
Evaluating the Conclusions
Let's analyze each conclusion based on the statements and the derived relationship:
-
Conclusion I: Some cakes are books
The first statement says "All books are cakes". If every book is a cake, then it must be true that at least some cakes (those that are books) are indeed books. This is a valid conversion from 'All A are B' to 'Some B are A'. Therefore, Conclusion I follows.
-
Conclusion II: No cake is books
This conclusion directly contradicts Statement 1 ("All books are cakes") and Conclusion I ("Some cakes are books"). Therefore, Conclusion II does not follow.
-
Conclusion III: Some apples are books
We derived that "All books are apples" ($B \subseteq A$). Similar to the logic for Conclusion I, if all books are apples, it must be true that at least some apples (those that are books) are books. This is a valid conversion from 'All A are B' to 'Some B are A'. Therefore, Conclusion III follows.
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Conclusion IV: All apples are books
This is the converse of the derived statement "All books are apples". We know that the set of books is a subset of the set of apples ($B \subseteq A$), but this doesn't mean the set of apples is entirely contained within the set of books ($A \subseteq B$). There could be apples that are not books. Therefore, Conclusion IV does not follow.
Final Assessment
Based on the analysis:
- Conclusion I follows.
- Conclusion III follows.
Since Conclusions I and III are the only ones that logically follow from the given statements, the correct option is the one stating that only I and III are valid.
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. - 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 Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the
statements.
Statements:
All furs are rabbits.
All furs are plants.
Conclusions:
(I): Some rabbits are plants.
(II): All plants are furs.
