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Question

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.

The correct answer is
Only conclusion (I) follows

Analyzing the Statements

We are given two statements about the relationship between 'furs', 'rabbits', and 'plants':

  • Statement 1: All furs are rabbits. This means that the set of all 'furs' is entirely contained within the set of 'rabbits'. In set notation, if F represents the set of furs and R represents the set of rabbits, then $ F \subseteq R $.
  • Statement 2: All furs are plants. Similarly, this means that the set of all 'furs' is entirely contained within the set of 'plants'. If P represents the set of plants, then $ F \subseteq P $.

From these two statements, we know that the set 'Furs' is a subset of both 'Rabbits' and 'Plants'. This implies that any member belonging to the set 'Furs' must also be a member of the set 'Rabbits' and the set 'Plants'. The intersection of Rabbits and Plants must contain Furs: $ F \subseteq (R \cap P) $.

Evaluating Conclusion (I): Some rabbits are plants

This conclusion states that there is at least one individual that is both a rabbit and a plant.

Based on our analysis of the statements:

  • We know $ F \subseteq R $ and $ F \subseteq P $.
  • This means that any element in F is also in R and also in P.
  • Therefore, the elements in F form the intersection of R and P.
  • If we assume that the set 'Furs' is not empty (which is a standard assumption in such logical problems unless stated otherwise), then there must be elements that are common to both 'Rabbits' and 'Plants'.
  • Thus, the statement "Some rabbits are plants" logically follows. Symbolically, $ \exists x (Rabbit(x) \land Plant(x)) $ is true if $ F \neq \emptyset $.

Evaluating Conclusion (II): All plants are furs

This conclusion states that the set of all 'plants' is entirely contained within the set of 'furs'. In set notation, this would mean $ P \subseteq F $.

Let's examine if this follows from the given statements ($ F \subseteq R $ and $ F \subseteq P $):

  • The statements tell us that Furs are Plants ($ F \subseteq P $), but they do not provide any information about the relationship in the reverse direction.
  • It is possible for the set 'Plants' (P) to be larger than the set 'Furs' (F). There could be plants that are not furs.
  • For example, consider: Furs = {Fox Fur}, Rabbits = {Rabbit A, Fox Fur}, Plants = {Plant X, Fox Fur}. Here, all furs are rabbits and all furs are plants. However, Plant X is a plant but not a fur.
  • Therefore, the statement "All plants are furs" does not necessarily follow from the given statements.

Final Deduction

Based on the analysis:

  • Conclusion (I) logically follows from the statements.
  • Conclusion (II) does not logically follow from the statements.

Therefore, only conclusion (I) follows.

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Important Questions from Syllogism (Notes)

  1. 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.

  2. 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.
  3. 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:
  4. 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 ?
  5. 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
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