Syllogism Questions and Answers

Syllogism Questions

Syllogism can be discussed as a kind of reasoning where an assumption is taken from two outlined or assumed offers. It is more of a logical reasoning instead of inductive reasoning. It is identified that most of the crucial sections of the exam includes syllogism in reasoning. 

Syllogism Questions

Rules for solving Syllogism Questions

One can face a lot of issues concerning the kind of sentence that may lead to the kind of conclusion. However, if you are thoroughly well aware of the rules mentioned below along with their correct use, then you are expected to commit no blunders while solving the questions. Check out the below rules:

–> Universal Positive Statement

To begin with universal signifies something that is appropriate to all as well as optimistic ways, such as the ‘yes’ kind of format. A universal positive statement specifies a little positivity relevant to all the things in that group. The positive category is signified by the alphabet ‘A’. These statements begin with All, Each and Every.

–> Universal Negative Statement

In this situation, the mere dissimilarity from the last type is that, in this situation, the sentence carries a negative meaning. It implies that it refers to that kind of sentence, which is common and giving a pessimistic expression. Such kinds of sentences start with No, Not a single, None of the, and more. These sentences are denoted by the letter ‘E’.

–> Particular Positive Statement

In this situation, the given sentence offers a positive expression, however, it includes only a few things and not all. These kinds of sentences often starts with some, a few, any, and are symbolized by the letter ‘I’.

–> Particular Negative Statement

Here, the statement again covers only some items, but it gives a negative impression. These kinds of sentences are symbolizes by the letter ‘O’.

  • When there are two specific sentences, no universal assumption is imaginable.
  • When there are two positive sentences, no negative assumption is imaginable.
  • When there are two negative sentences, no positive assumption is imaginable.
  • When there are two specific sentences, no assumption can take place, apart from when an ‘I’ kind of sentence is provided as well as by retreating it an ‘I’ kind of assumption can be done.

Important formulas to remember:

  • Some + All= Some
  • Some + Some= No Conclusion
  • Some + No= Some Not
  • No + No= No Conclusion
  • No +All = Some Not Reversed
  • No + Some = Some Not ( Reversed )
  • Some Not/ Some Not Reversed + Anything= No Conclusion
  • No + All = Some not Reversed
  • All + Some = No Conclusion
  • All + All= All
  • All + No= No

Important Points

  • Syllogism is comprised of three components, those are – minor premise, major premise and conclusion.
  • The kind of syllogism which usually comprises these three elements is categorical syllogism. Although, two additional key types of syllogism are further present.

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Syllogism Questions and Answers

1. Statements:

Some dogs are bats.

Some bats are cats.

Conclusions:

Some dogs are cats.

Some cats are dogs.

Neither I nor II follows

Neither I nor II follows

60.29%

Only I follows

Only I follows

11.67%

Only II follows

Only II follows

3.92%

Both I and II follows

Both I and II follows

24.11%

Text solution:

Video solution:

2. Statements:

All buildings are chalks.

No chalk is toffee.

Conclusions:

No building is toffee
All chalks are buildings.

if either conclusion I or conclusion II is true.

if either conclusion I or conclusion II is true.

16.82%

if only conclusion II is true.

if only conclusion II is true.

15.68%

if only conclusion I is true.

if only conclusion I is true.

50.05%

if neither conclusion I nor conclusion II is true

if neither conclusion I nor conclusion II is true

17.45%

Text solution:

Video solution:

3.

Statements: 

All the harmoniums are instruments.

All the instruments are flutes.

Conclusions:

All the flutes are instruments.
All the harmoniums are flutes.

if only conclusion I is true.

if only conclusion I is true.

17.03%

if only conclusion II is true.

if only conclusion II is true.

60.23%

if either conclusion I or conclusion II is true.

if either conclusion I or conclusion II is true.

14.63%

if neither conclusion I nor conclusion II is true

if neither conclusion I nor conclusion II is true

8.11%

Text solution:

Video solution:

4. Statements:

Most CPUs are keyboards.

No keyboard is a Mouse.

All Mouses are CPU.

Conclusion:

  1. Some keyboards are CPU
  2. All CPU’s are Mouse
  3. No mouse is a keyboard
  4. Some Mouse are keyboard

if only conclusion I is true.

if only conclusion I is true.

13.23%

if only conclusion II is true.

if only conclusion II is true.

6.69%

if either conclusion I or conclusion II is true.

if either conclusion I or conclusion II is true.

11.56%

if neither conclusion I nor conclusion III is true

if neither conclusion I nor conclusion III is true

13.51%

Only I and III are true.

Only I and III are true.

55.01%

Text solution:


Video solution:

5. Statements:

All liquids are solids.

Some solids are gases.

All gases are clouds

Conclusion:

Some clouds are solids
Some clouds are liquids
Some gases are liquids
Some solids are clouds

if only conclusion III is true.

if only conclusion III is true.

9.45%

Only I and IV follows

Only I and IV follows

74.54%

if either conclusion I or conclusion II is true.

if either conclusion I or conclusion II is true.

8.38%

if neither conclusion I nor conclusion II is true

if neither conclusion I nor conclusion II is true

7.62%

Text solution:


Video solution:

6. Statements:

Some messages are whatsapp.

All Hikes are whatsapp.

All whatsapp are facebook.

Conclusion:

  1. Some facebook are messages
  2. All hikes are facebook
  3. Some messages are hikes
  4. Some message are facebook

Only I and II follow

Only I and II follow

7.82%

Only either III or IV follows

Only either III or IV follows

6.66%

Only I and either III or IV follow

Only I and either III or IV follow

16.64%

Only I, II and IV follows

Only I, II and IV follows

68.89%

Text solution:


Video solution:

7. Statements: 

Some Cats are Rats.

All bats are tables.

All Rats are Bats.

Conclusion:

  1. Some Cats are bats
  2. All bats are rats
  3. All tables are cats
  4. All bats are cats

Only III & IV follow

Only III & IV follow

6.15%

Only II follows

Only II follows

9.22%

Only  I  follows

Only  I  follows

75.95%

None follows

None follows

8.68%

Text solution:

Video solution:

8. Statements

Some cups are pots

All pots are tubes

Conclusions

  1. Some pots are cups
  2. Some tubes are cups

Only I follow

Only I follow

9.71%

Only II  follow

Only II  follow

8.63%

Both I and II follows

Both I and II follows

78.24%

None follow

None follow

3.42%

Text solution:

Video solution:

9. Statements

Some bags are books

All books are boxes

Conclusions

  1. All Bags are boxes
  2. No Book is boxes

Only I follows

Only I follows

11.75%

None follows

None follows

70.71%

Only II follows

Only II follows

8.02%

Only either I or II follows

Only either I or II follows

9.51%

Text solution:

Video solution:

10. Statements:
Some papers are pens.
All pencils are pens.
Conclusions:
1. Some pens are pencils.
2. Some pens are papers.

Both (1) and (2) follow

Both (1) and (2) follow

67.29%

Only (2) conclusion follows

Only (2) conclusion follows

21.5%

Either (1) or (2) follows

Either (1) or (2) follows

6.73%

Neither (1) nor (2) follows

Neither (1) nor (2) follows

4.49%

Tick & cross Method :

Conclusions: 1. Some pens are pencils. - Possible - Because All pencils are pens.

Conclusions: 2. Some pens are papers. - Possible - Because Some papers are pens.

OR

Note: Here, a conclusion is definite if it can be shown in a diagram drawn with least-possibilities. If a conclusion can’t be shown in least-possibilities diagram then the conclusion is possible but not definite.

On drawing least-possibilities Venn-diagram:

Conclusions:

1. Some pens are pencils. ⇒ It’s, definitely, true.

2. Some pens are papers. ⇒ It’s, definitely, true.

Hence, both 1 and 2 follow

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