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# Reasoning: Syllogism Possibility with Venn Diagram

### Syllogism: Possibility

Dear students,
In this post, we will provide you the shortest possible way to solve syllogism questions very quickly and fast.
Our main aim is “HOW TO SOLVE SYLLOGISM POSSIBILITY QUESTIONS IN LESS TIME”.

These questions are totally based upon the logic. If we solve these questions with the help of venn diagram then we can get the conclusion very easily.

Remember that these type of venn diagrams are just a medium to solve such questions very fast questions can have many ways to draw a venn diagram by a statement given in questions, but we have to draw the easiest diagram first because it will enable us to solve the question in less time.

TYPE 1
Representation of “ALL M are P“
Picture

Here, the whole circle denoting M (all M) lies inside the circle denoting. The other possibility is as picture given below
picture

TYPE 2
Representation of “No M are P”
Picture

Here the circle denoting M and P do not intersect at all and therefore, truly represents
“No M are P”

TYPE 3
Representation of “Some M are P”
picture

Here, it is clear from the picture that shaded part of M is some part of P and shaded part of P is some part of M. Thus “Some M are P”. Similarly, unshaded part of M is not P and unshaded part of P is not M.Thus it represent “Some M are not P”

TYPE 4
Representation of “Some M are not P”
picture

### some questions based on possibility  (asked in IBPS/SBI/RBI exam)

STATEMENTS

Some seeds are flowers
All flowers are tree
only trees is leaves
Some leaves are branches

Conclusions:
1.All branches being flowers is a possibility
2.Some leaves are seeds
3.Some leaves being flowers is a possibility

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I and II do not follows
2.Only I and III do not follows
3.Only II and III do not follows
4.Only II does not follows
5.None of these

(4) Only II does not follows

STATEMENTS

All flowers are toys
Some toys are trees
Some ants are trees

Conclusions:
1.Some ants are toys
2.Some trees are flowers
3.Some flowers being ants is a possibility

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I do not follows
2.Only II do not follows
3.Only I and II do not follow
4.Only III does not follow
5.All I, II, and III do not follows

(3) Only I and II do not follow

STATEMENTS

Some seeds are balls
All balls are bats
Some tigers are balls

Conclusions:
1.Some bats not being seeds is a possibility
2.Some balls being tiger is a possibility
3.Some bats being tiger is a possibility

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I does not follow
2.Only II does not follow
3.Only II and III do not follow
4.Only III does not follow
5.None of these

(3) Only II and III do not follow

STATEMENTS

No coke are holder.
All holders are lamps
Some lamps are desks
Some desk are pens

Conclusions:
1.All desks being coke is a possibility
2.All lamp being coke is a possibility
3.Some desks are not coke
4.Some coke are not holder.

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I and II follows
2.Only I follows
3.Only              III and IV follows
4.Only II and III follows
5.None of these

(3) Only III and IV follows

STATEMENTS

All cars are tents
No cars is jugs.
No jugs is glasses
No glasses is pots

Conclusions:
1.All pots being tents is a possibility
2.All glasses being cars is a possibility
3.Some jugs are tents
4.No jugs is tents

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I follows
2.Only II follows
3.Both I and II follows
4.Only I, II and either III or IV follows
5.None of these

(4) Only I, II and either III or IV follows

STATEMENTS

Some train are light.
Some light are fast.
Some fast are noise
Some noise are soft

Conclusions:
1.Some light are soft.
2.Some soft being train is a possibility
3.Some fast not being noise is a possibility

Read all the conclusions and then decide which of the given conclusions logically does not follow
1.Only I and II do not follows
2.Only I and III do not follows
3.Only I does not follows
4.Only I, II and III do not follows
5.None of these

(3) Only I does not follows

### Syllogism Possibility With Notation Method

Syllogism: Possibility

Questions based on possibility cases questions are often asked in bank exams. To solve syllogism questions on possibilities, following points should be kept in mind:

(1) When definite conclusions (either definitely true or definitely false) can be drawn from the given propositions, they are certainties. It is to be noted that conclusions can be drawn either by ‘immediate inference’ ( implication or conversion) or by ‘mediate inference’ (combining pair of aligned propositions).

For example, take an A-type proposition as given below:
All S are P
For this statement, following are the definite conclusions:
i) All S are P -> conversion -> Some P are S [ Definitely True ] [ Since, on conversion of A-Type statement, we obtain I-type of statement ]

ii) All S are P -> implication -> Some S are P [ Definitely True ]

iii) No S are P [ Definitely False ]

iv) Some S are not P [ Definitely False ]

Therefore, the above drawn conclusions are cases of certainties.

(2) When definite conclusions cannot be drawn from the pair of aligned statements (mediate inference), cases of possibilities exist.
It should be noted that there are only six cases where a conclusion can be drawn. These cases are as given below:
A + A = A
A + E = E
E + A = O*
E + I = O*
I + A = I
I + E = O

Except the above mentioned cases, in all other cases, possibilities exist.

A + I = _
A + O = _
E + E = _
E + O = _
I + I = _
I + O = _
O + [A or E or I or O ] = _
Note: ‘_’ stands for ‘No conclusion’.
Now, we analyse the different cases of possibilities in the following pages:

Immediate Possibilities

A-Type [ All S are P ]

I. Implication Conclusions:
i) Some S are P [ True ] ii) Some S are not P [ False ] iii) No S are P [ False ] The above three conclusions are either definitely true or definitely
false.

II. Conversion
We know that A-Type of statements can be converted to I-Type of
statements. Therefore, All S are P -> conversion -> Some P are S.
Hence, ‘Some P are S’ is a definite conclusion. But ‘All P are S’ is
a possibility.

E-Type [ No S are P ] I. Implication Conclusions:
i) All S are P [False] ii) Some S are P [False] iii) Some S are not P [True] The above conclusions are either definitely true or definitely false.

II. Conversion
No S are P(E) -> conversion -> No P are S(E). Therefore, ‘No P are
S’ is a case of certainty.

I-Type [Some S are P] I. Implication Conclusions:
i) No S are P [False] The above conclusion is definitely false.

Cases of Possibilities:
i) All S are P [Doubtful] ii) Some S are not P [Doubtful] All the above statements are cases of possibilities.

II. Conversion
Some S are P(I) -> conversion -> Some P are S(I). The above statement
is a definite conclusion obtained by conversion of the given I-Type of
statements as given below:
i) All P are S
ii) Some P are not S

O-Type [Some S are not P] I. Implication Conclusions:
i) All S are P [False] The above conclusion is definitely false.
Cases of Possibility:
i) No S are P [Doubtful] ii) Some S are P [Doubtful]

The above statements are cases of possibilities.

II. Conversion
We know that O-type of statements cannot be converted. Therefore,
there can be no definite conclusion from the conversion of O-type of
statements. However, the following possibilities exist:
i) All P are S
ii) No P are S
iii) Some P are S
iv) Some P are not S

Note: Here, for the cases of possibilities, we consider O-Type and O*-
Type statements alike. For this reason we do not take up O*-Type as a
separate case.

Summary
Cases of Possibility
A-Type [All S are P] i) All P are S

I-Type [Some S are P] i) All S are P
ii) Some S are not P
iii) All P are S
iv) Some P are not S

O-Type [Some S are not P] i) No S are P
ii) Some S are P
iii) All P are S
iv) No P are S
v) Some P are S
vi) Some P are not S

Mediate Possibilities

When we have been given any of the following types of pair of aligned
statements, cases of possibilities exist:

A + I; A + O; E + E; E + O; I + I; I + O; O + [ A or E or I or O ]

Suppose, we have the following propositions:

1. A + I
All S are P Some P are Q
2. A + O
All S are P Some P are not Q
3. E + E
No S is P No P is Q
4. E + O
No S is P Some P are not Q
5. I + I
Some S are P Some P are Q
6. I + O
Some S are P Some P are not Q

Note: Similarly, we can write a pair of aligned statements for O + A, O + E, O + I and O + O also.

We know that from the above pairs of aligned statements, definite conclusions cannot be drawn. But some relationships between S and Q exist and we cannot say definitely that the relationships do exist.

Therefore, cases of possibility arise. That is there are the possibilities that some relationships between S and Q exist. For any of the above pairs of aligned statements, following are the all standard cases of possibilities that exist between S and Q.

a) All S are Q
b) Some S are Q
c) Some S are not Q
d) All Q are S
e) Some Q are S
f) Some Q are not S

‘Either…..or’ Cases in Possibility

We will try to understand the ‘Either….or’ cases of possibility by examples as given below:

Ex 1: Statements: Some P are Q
All Q are R.
No R is S.

Conclusions:
I. All S being P is a possibility.
II. All P being R is a possibility.

Explanation:
Some P are Q + All Q are R + No R is S = I + A + E = ( I + A) + E = I + E = O = Some P are not S. From this O-Type of conclusion there is a possibility of all S being P.

Therefore, conclusion I follows. Again, Some P are Q + All Q are R = I + A = I = Some P are R. From this conclusion, possibility of all P being R exists.

Therefore, conclusion II follows. But if II is possible, I can’t be possible. How ? Then All P are R + No R is S = A + E = E = No P is S. Thus, both conclusions I and II can’t follow simultaneously.

Therefore, ‘Either I or II follows’ will be the correct answer.

Ex 2: Statements: Some P are Q.
All Q are R.
No R is S.

Conclusions:
I. All P being R is a possibility.
II. All S being P is a possibility.

Explanation:

Some P are Q + All Q are R = I + A = I = Some P are R => All P being R is a possibility.

Therefore, conclusion I follows. Again, Some P are Q + All Q are R + No R is S => All S being P is a possibility. Therefore, conclusion II follows. But, conclusions I and II both cannot be true simultaneously.

If I follows, All P are R + No R is S = A + E = E = No P is S. Hence II can’t follow. Hence, ‘Either I or II follows’ will be the correct answer.

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