Syllogism at its Best

Piscine Molitor (Pi) again provided us one of his magnificent post on "Syllogism at its Best". So, here we are providing you the same. Don't forget to thank him!!!


I’m sure most people would have tried to do these questions, with the wrong conclusions. What they did are, they first made all the conclusions and then they headed on the conclusion, seeing if they’re fitting in their circles or not. Then they ticked the right conclusions, crossed the wrong ones, and whoosh, wrong answer!

Now, in this post, I’d like make you understand this trick of picking up the right conclusions!! The trick is “One statement has many conclusions!!”

Now, let’s start from the basic statements

Statement 1: All A are B

Now, let’s try all these conclusions if they fit in this statement

1. Some A are B
2. No A are B
3. Some A are not B
4. All B are A
5. Some B are A
6. No B are A
7. Some B are not A

Is conclusion 1 following?
Yes! Of course! All A are B, that means Some A are Definitely B

Is conclusion 2 following?
Of course not!

What about 3rd?
Yes yes. Not following

4th?
Well, can follow, if A encircles B, i.e. All A are B and All B are A

5th?
Of course, some B are A

6th?
Bullshit conclusion. How can no B are A

7th?
Well, look at 4th conclusion. Its possible that All B are A if A also encircles B. In that case, Some B are not A will not follow. So, there’s a possibility that this 7th conclusion will follow. Understood?

Statement 2: Some A are B

Now, let’s try all these conclusions if they fit in this statement

1. All A are B

2. No A are B

3. Some A are not B

4. All Bare A

5. Some B are A

6. No Bare A

7. Some B are not A

Is conclusion 1 following?

Could follow.

2nd?

Impossible.

3rd?

It won’t follow in all the cases, but it’s possible. 

4th?

Again, it’s possible.

5th?

Yes. Follow. In all cases.

6th?

Impossible.Nahinahinahi!

7th?

It could be possible. Won’t follow in all the cases, but yes, it also could be possible.

Statement 3: No A are B

Now, let’s try all these conclusions if they fit in this statement

1. All A are B

2. Some A are B

3. Some A are not B

4. All Bare A

5. Some B are A

6. No Bare A

7. Some B are not A

Conclusion 1 following?

Of course not!

2nd?

Haha..

3rd?

No A are B, then Some A are also Not B.. Yes, following!

4th?

Clearly, not following!

5th?

What the hell. Not following!

6th?

Now this is class. Yes, follows!

7th?

Of course will follow! No A are B only means, No B are A, which also means, Some B are not A

Statement 4: Some A are not B

Now, let’s try all these conclusions if they fit in this statement

1. All A are B

2. Some A are B

3. No A are B

4. AllB are A

5. Some B are A

6. No Bare A

7. Some B are not A

Is conclusion 1 following?

Of course not!

2nd?

It could be possible! Not in all cases, but it could be possible

3rd?

Again, could be possible!

4th?

Yes, yes. Could be possible!

5th?

Not in all cases, but could be possible!

6th?

Again, it also could be possible!

7th?

Again, possible!

Now, let’s solve some basic questions based on all the things that we’ve just learned.

Question 1:

Statements: 

All buckets are mugs.  

All lunch boxes are pencil boxes.  

Some pencil boxes are mugs.  

Some buckets are not drums.

Conclusions: 

I. All mugs are lunchboxes.  

II. All lunchboxes are buckets.

III. Some lunchboxes are mugs. 

IV. Some drums are not mugs.

1? Not follows

2? Not follows

3? Not follows

4? Not follows

Question 2: 

Statements: 

Some chairs are tables.  

Some desks are benches.

All benches are tables.  

Some woods are not desks.

Conclusions: 

I. Some benches are desks.  

II. Some tables are benches.

III. Some woods are not benches. 

IV. Some desks are tables.

1? Yes

2? Yes

3? Not follows

4? Yes

Question 3:

Statements: 

No bank is a market.
Some markets are offices.

All restaurants are offices.  

Some banks are rooms.

Conclusions: 

I. Some markets are not rooms. 

II. Some offices are not banks.

III. Some restaurants are markets. 

IV. Some rooms are restaurants.

1? Not Follows

2? Yes. Some offices which are Market cannot be Banks

3? Not follows

4? Not follows

Question 4:

Statements: 

All ones are twos.

Some threes are fours.

All three are ones.   

All five are fours.

Conclusions: 

I. Some fives are threes.  

II. Some ones are fives.

III. Some twos are fives.  

IV. Some twos are fours

1? Not follows

2? Not follows

3? Not follows

4? Yes. Follows

Thanks Pi!!

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