Syllogism Based Questions | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Syllogism

Syllogism is a important chapter in verbal reasoning. It helps to build up the logic of your brain. In exams like BANK, RRB, CAT, MAT and other competitive exams this chapter based question has given. This chapter based question has given to checks the logical ability of students.

we can solve this question with the help of Venn diagram. Using this Venn diagram we solve each and every questions and we get conclusion easily. According with statement we need to draw Venn diagram.

There are different types of statements has given one is definite case as conclusion and another is possibility case and you have to draw different Venn diagram. Before going to conclusion you have to draw a simple Venn diagram, which help you to get conclusion easily.

We provide you some short cut tricks that help you to solve it in a simple way and also take less time to solve questions:

• All DOGS are CATS
  
• Some DOGS are CATS
• No DOG is CATS
  
• Some DOGS are not CATS
  

Solved Example

In each of the below questions given Two statements are followed by two conclusion which numbered 1 and 2. You have to consider the two given statements to be true even if they seem to be at variance from commonly known facts and choose the correct option about conclusions which logically follows from the two given statements.
(a) only conclusion i follow
(b) only conclusion ii follow
(c) either i or ii follows.
(d) neither i nor ii follows.
(e) both i or ii follows.

Example: Statements:

• All cows are goat
• All goat are dog

Conclusions:

1. All cows are dog
2. Some cows are dog

Ans: (e)
Explanation: 

• Conclusion 1: "All cows are dogs."

  • Since all cows are goats (from Statement 1) and all goats are dogs (from Statement 2), it logically follows that all cows must be dogs. This conclusion is true.

• Conclusion 2: "Some cows are dogs."

  • If all cows are dogs (as derived from Conclusion 1), then it's also true that some cows are dogs. This conclusion is also true because "some" is a subset of "all."

Either case

Example: Statements:

• All cows are dogs
• Some dogs are goat
• No goat are rat

Conclusions:

• Some rat are cows
• No rat are cows

Ans: (b)

Explanation: 

• Conclusion 1: "Some rats are cows."

  • To have "Some rats are cows" to be true, there must be an overlap between rats and cows.
  • However, from the statements, cows are dogs, and no goat is a rat. But nothing directly connects cows with rats, and since goats (which are dogs) do not overlap with rats, cows cannot overlap with rats.
  • This conclusion is false.

• Conclusion 2: "No rats are cows."

  • Based on the statements, there is no direct link between cows and rats, but the statements imply that cows, being dogs, do not have any connection to rats (because goats, which some dogs are, do not overlap with rats).
  • Therefore, this conclusion is true.

Possibility

In syllogism possibility is a type of conclusion where you need to draw Venn diagram and according with statements and also verify its true or false.

• Note: According to conclusion you have to draw possibility figure without affecting the statements.
• the possibility type questions has give some time positive or negative way.

Example: Statements:

• All books are pen
• Some pen are pencil
• No pencil is Eraser

Conclusions:

1. All books being Eraser is possibility
2. Some books being Eraser possibility

Ans: (d)

Analyzing the Conclusions:

1. Conclusion 1: "All books being erasers is a possibility."

   • To evaluate this, consider the relationships:
     • All books are pens.
     • Some pens are pencils, but no pencil can be an eraser.
     • Since some pens are pencils and no pencil is an eraser, books (which are pens) cannot be erasers if they are related to pencils. Thus, the possibility of all books being erasers is not possible.
   • This conclusion is false because the relationship between pencils and erasers prevents all books (which are pens) from being erasers.

2. Conclusion 2: "Some books being erasers is a possibility."

   • Similarly, since all books are pens, and no pencil (which overlaps with pens) can be an eraser, no books can be erasers either.
   • This conclusion is also false because the same logic applies: if no pencil can be an eraser, then the books, which are pens and overlap with pencils, cannot be erasers.

Final Answer:

• Conclusion 1 ("All books being erasers is a possibility") is false.
• Conclusion 2 ("Some books being erasers is a possibility") is false.