All Exams Test series for 1 year @ ₹349 only
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.

Was this answer helpful?

Important Questions from Syllogism (Notes)

  1. 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.
  2. Take the given statements to be true even if they seem to be at variance with commonly known facts. Then decide which of the given conclusions logically follow the given statements. 

    Statements : 

    0% chairs are tables. 

    All computers are chairs. 

    Some books are tables. 

    Conclusions : 

    I. Not a single table is a computer. 

    II. Some books are not chairs.

  3. Directions: Study the following Bar-chart and the data provided to answer the questions that follow: Sales of 3-different companies selling T-Shirts for the years from 2006 to 2009 are given. How much percentage of sales decreased for Brand X T-shirt in 2009 compared with 2007?

  4. Statements: 

    All herbivores are carnivores.

     Some carnivores are omnivores. 

    Conclusions:

     i) Some herbivores are omnivores.

     ii) Some carnivores are herbivores.

  5. Statements: 

    All sweets are snacks. 

    All snacks are crisps. 

    All crisps are tasty. 

    Conclusions: 

    i) All sweets are crisps. 

    ii) All snacks are tasty.

Need Expert Advice?

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App