Syllogism-Based Questions

Syllogism

Syllogism is an important topic in verbal reasoning that helps you think logically and draw conclusions from given statements. It appears regularly in competitive exams to test how well you can connect information and decide what must be true.

Most syllogism questions are best solved with Venn diagrams. A clear Venn diagram shows how the groups in the statements are related, making it much easier to check whether the conclusions follow.

Syllogism conclusions are generally of two kinds: definite conclusions (those that must be true given the statements) and possible conclusions (those that may be true without contradicting the statements). Before judging a conclusion, always construct the simplest Venn diagram that represents the statements; this simplifies the subsequent analysis.

Shortcut Tricks 

Some shortcut tricks will help you solve it simply and also take less time to solve questions
The following given cases have the respective Venn diagram which will help in solving questions of such kind 

1. All DOGS are CATS
   
   
2. Some DOGS are CATS
3. No DOG is CATS
   
4. Some DOGS are not CATS
   

Solved Examples

• In each of the questions below, two statements are followed by two conclusions 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 1: 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."
    Therefore, Conclusion i and ii follows.

Example 2: Statements:

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

Conclusions:

1. Some rats are cows
2. No rats are cows

Ans: (b)

Conclusion 1: Some rats are cows

There is NO link at all between rats and cows.

From:

All cows → dogs

Some dogs → goats

No goats → rats

You cannot infer existence of rats inside cows.

This conclusion does NOT follow.

Conclusion 2: No rats are cows

Again, no direct relationship between cows and rats is given.

It is possible that:

Some cows are rats

Or no cows are rats

So this is also NOT definite.

Answer: (d) Neither conclusion I nor II follows

Possibility

A possibility question asks whether a particular configuration can be true without contradicting the given statements. To evaluate a possibility, construct a Venn diagram that satisfies the statements and then check if the proposed possibility can coexist with those diagrams.

Note: While checking a possibility-based conclusion, draw a Venn diagram that satisfies both the statements and the possibility, ensuring the original statements are not violated.

Possibility conclusions may be phrased positively (something is possible) or negatively (something is impossible). Testing involves verifying existence of at least one model (Venn configuration) where the possibility holds.

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)

• All books being erasers is a possibility.

  • Explanation: Since all books are pens, and some pens are pencils, but no pencils are erasers, it is possible for books (which are pens) to be erasers as long as they are not among the pens that are pencils. There is no statement preventing all books from being erasers.

• Some books being erasers is a possibility.

  • Explanation: Even if not all books are erasers, the fact that some pens are not pencils allows for the possibility that some of these pens (which are books) could be erasers without violating any of the given statements.