Login

Syllogisms- Simple Method

There is a classical way to solve the syllogisms i.e., Venn Diagram. If you feel good with venn, skip this


Venn diagramsAll A are B –> universal propositions

Some A are B –> particular propositions

No A are B–> universal propositions

Some A are not B –> particular propositions

Premise :1 -> All A are B

Premise: 2 -> All B are C

Here, B repeats twice, this is called Middle term and in most of the cases this won’t be in your conclusions.

Given any statements convert them in this format(A-B, B-C).




Before going to formulae one should remember these,

All A are B can also be written as, Some B are A;

Some A are B –> Some B are A

No A are B –> No B are A

A Question can be in any type but you have to convert the given 2 statements as A are B and B are C

Eg:



All dogs(A) are Animals(B)

All men(C) are Animals(B)

this is not our classical way, so covert the second statement into our classical way. So second statement can be converted as “some animals are men”.

After converting any two statements into the classical way, apply the below rules.

“No conclusion” cases will give rise to ” either or” conclusions. Those will be dealt in complex problems down. Till then remember ” No conclusion –> Either -or”

Statement 1

Statement 2

Conclusion

Rule 1

All

All

All

Rule 2

All

Some

No Conclusion

Rule 3

All

No

No

Rule 4

Some

All

Some

Rule 5

Some

Some

No Conclusion

Rule 6

Some

No

No Conclusion

Rule 7

No

All

No Conclusion

Rule 8

No

Some

No Conclusion

Rule 9

No

No

Invalid

So lets compare both methods and draw some conclusions



  1. All dogs are asses.
  2. All asses are bulls.

Conclusions:

  1. Some dogs are not bulls.
  2. Some bulls are dogs.
  3. All bulls are dogs.
  4. All dogs are bulls.

Solution:

All and All –> All (Rule 1)

so “All dogs are bulls”. and this conclusion can be written as “some bulls are dogs”.

Ans: 2, 4 are correct.


On the basis of both statements, the following one diagram is possible.

From the diagram it is clear that (2) and (4) conclusions logically follow.


Let’s take another one,

Some keys are staplers. Some staplers are stickers. All the stickers are pens.Conclusions:

  1. Some pens are staplers.
  2. Some stickers are keys.
  3. No sticker is key.
  4. Some staplers are keys.
A. Only (1) and (2)
B. Only (2) and (4)
C. Only (2) and (3)
D. Only (1) and (4)

If you have 3 statements, take a pair according to conclusions given

so, Some pens are staplers; take last 2 statements.

Some staplers(A) are stickers(B) and All the stickers(B) are pens(C).

some and all –> some( Rule 4); –> some staplers(A) are pens(C) this can be converted into some pens(C) are staplers(A). –> Conclusion 1 is true.

conclusion 2; Some stickers are keys. first 2 statements

Some keys(A) are staplers(B). Some staplers(B) are stickers(C).

some and some –> No conclusion(Rule 5); conclusion 2 wrong.

conclusion 3; No sticker is key. first 2 statements

same as above No conclusion

conclusion 4; Some staplers are keys. take statement 1

Some keys are staplers –> some staplers are keys; so this conclusion is true.

Finally go with the option D.

Practice More and when you feel confident on above concepts touch “either-or” cases. (Practising is the key here )

No conclusion –> Either -or

I divided all the 5 No conclusion cases into 2 sets;

All four except the below one falls under set-1

ALL-SOME is another set-2

Set-1-The given two conclusions give rise to ” Either No or Some”

Set-2- “Either Some B are C or Some A are C”

All the results are examined using venn diagrams, you can recheck them.



the same table can be re-written as

Statement 1 Statement 2 Conclusion Either-or
Rule 1 All All All
Rule 2 All Some No Conclusion Some A are C; Some B are C
Rule 3 All No No
Rule 4 Some All Some
Rule 5 Some Some No Conclusion Some-No
Rule 6 Some No No Conclusion Some-No
Rule 7 No All No Conclusion Some-No
Rule 8 No Some No Conclusion Some-No
Rule 9 No No Invalid Invalid

 

So lets take the above same example,

Some keys are staplers. Some staplers are stickers. All the stickers are pens.Conclusions:

  1. Some pens are staplers.
  2. Some stickers are keys.
  3. No sticker is key.
  4. Some staplers are keys.
A. Only (1) and (2)
B. Only (2) and (4)
C. Only (2) and (3)
D. Only (1) and (4) and either (2) or (3)

If you have 3 statements, take a pair according to conclusions given

so, Some pens are staplers; take last 2 statements.



Some staplers(A) are stickers(B) and All the stickers(B) are pens(C).

some and all –> someRule 4); –> some staplers(A) are pens(C) this can be converted into some pens(C) are staplers(A). –> Conclusion 1 is true.

conclusion 2; Some stickers are keysfirst 2 statements

Some keys(A) are staplers(B). Some staplers(B) are stickers(C).

some and some –> No conclusion(Rule 5) and Either Some keys(A) are stickers(C) or No keys(A) are stickers(C).

conclusion 3; No sticker is key. first 2 statements

same as above No conclusion;

conclusion 4; Some staplers are keystake statement 1

Some keys are staplers –> some staplers are keys; so this conclusion is true.

Finally go with the option D.

Look at the options, if there is either-or options, then take that extra last step or else take it as No conclusion.

Practice more, if you have any doubts throw a comment. I’ll try to make it simple for you.

0 responses on "Syllogisms- Simple Method"

Leave a Message

Your email address will not be published. Required fields are marked *

About Us

Go Prep An Online Educational Platfom    

Don’t Miss Any Updates

Contact Us

22-49/4, SR RESIDENCY

KAMALANAGAR,DILSUKNAGAR,

HYDERABAD-500060

PH N0. : +91 9030832730

E-MAIL : admin@goprep.in

top
Krishna's Group. All Rights Reserved
X