Syllogism at its best - Part - II

In possibility questions, the examiner asks if there exists any such case (diagram) where this conclusion is valid. So, you job is to find out this case. If there exists at least one such case, then the conclusion holds true. If not, then the conclusion is false. As simple as that!

Keeping this and also the previous Syllogism Post in mind, let’s solve some possibility questions.

Abbreviations that I used:

Basic Diagram = BD

Modified Diagram = MD

Question 1:

 Statements:

A. All flowers are trees

B. Some trees are houses

C. All houses are wheels

Let’s first make a BD according to these statements.

Conclusions:

1. At least some wheels are trees

2. Some trees are flowers

3. All wheels are flower is a possibility

Now, see the BD,

Conclusion 1 clearly follows. 

Conclusion 2 also clearly follows. 

But, what about Conclusion 3?

Let’s make a MD and see if it follows or not!

In the MD, we can clearly see that all the statements are still valid, and Conclusion 3 also is following. So, Conclusion 3 follows. 

• 1? Follows
• 2? Follows
• 3? Follows

Understood?

Let’s now solve another question!

Question 2:

Statements:

A. Some desks are chairs

B. Some chairs are pens

C. Some pens are drawers

First, make a BD according to these statements. 

Conclusions:

1. At least some drawers are desks

2. There is a possibility all drawers are chairs

3. No drawer is a chair

Now, see the BD

Conclusion 1 clearly doesn’t follow. 

But, what about Conclusion 2?

Let’s make a MD

See the MD, Conclusion 2 follows in it.

And if there is a possibility that All drawers are chairs, then how could No drawer is a chair follow?

So, Conclusion 3 will not follow! 

• 1? Doesn’t follows
• 2? Follows
• 3? Doesn’t follows

Understood?

Let’s solve another one!

Question 3:

Statements:

A. All politicians are corrupt

B. Some politicians are honest

C. No leader is honest

First, make a BD according to these statements.

Conclusions:

1. Some politicians are not leader

2. All honest being corrupt is a possibility

3. Some leaders are not corrupt

Now, see the BD, 

Some politicians, which are honest (Red Portion), cannot beleaders. 

So, Conclusion 1 clearly follows. 

But, what about Conclusion 2?

Let’s make a MD.

See the MD, Conclusion 2 clearly follows!

What about conclusion 3?

Let’s make another MD.

See the last diagram, All leaders are corrupt could be a possibility! So, Conclusion 3 doesn’t follow. 

• 1? Follows
• 2? Follows
• 3? Doesn’t follows

Understood?

Question 4:

Statements:

A. Some people are intelligent

B. All intelligent are honest

C. No intelligent is smart

First, make a BD according to these statements.

Conclusions:

1. Some honest are not smart

2. All people being honest is a possibility

3. Some honest are people

Now, see the BD, 

Some honest, which are intelligent (Red Portion), cannot be smart. 

So, Conclusion 1 follows.

But, what about Conclusion 2?

Let’s make a MD.

See the MD, Conclusion 2 clearly follows.

Conclusion 3 also follows. 

• 1? Follows
• 2? Follows
• 3? Follows

Understood?

Question 5:

Statements:

A. Some writers are poets

B. All poets are singers

C. Many singers are actors

D. No singer is a dancer

First, make a BD according to these statements.

Conclusions:

1. Some writers are singers

2. Some actors are not dancers

3. All poets being actor is a possibility

4. No poet is a dancer

See the BD, 

Conclusion 1 clearly follows.

Also, some actors, which are singers (Red Portion), cannot be dancers. 

So, Conclusion 2 also follows.

But, what about Conclusion 3?

Let’s make a MD.

See the MD, 

Conclusion 3 clearly follows.

Also, since no singer is a dancer, so, no poet is a dancer. 

Hence, Conclusion 4 is also following!

• 1? Follows
• 2? Follows
• 3? Follows
• 4? Follows

Understood?

PS: Try re-doing these questions again if you still feel confused. Confusions will be clear this way!