1. Introduction About Syllogism
- Syllogism is a verbal reasoning type problem, which is an important topic and one-two questions will be asked in UGC NET Exam. These types of questions contain two or more statement and these statements are followed by the number of conclusions. You have to find which conclusions logically follows from the given statements.
The best method of solving the Syllogism’s problem is through Venn Diagrams. There are four ways in which the relationship could be made.
(a). Category 1: All A are B: Means the whole circle representing A lies within the circle representing B.
For example, All boys are men.
(b). Category 2: No A is B: Means that circles representing A and B does not intersect at all.
For example, No ball is a bat.
(c). Category 3: Some A is B: Means that some part of the circle represented by A is within the circle represented by B.
This type of (category 3) statement gives the following conclusions:
(i) Some A are B also indicates that – Some A are not B
(ii) Some A is B also indicates that – All A are B.
(iii) Some A is B also indicates that – All B are A.
(iv) Some A is B also indicates that – All A are B and All B are A.
For e.g.: Some mobiles are phones.
(d). Category 4: Some A is not B: Means that some portion of circle A has no intersection with circle B while the remaining portion of circle A is uncertain whether this portion touches B or not.
(i) Some A is not B also indicates that – Some A are B.
(ii) Some A is not B also indicates that – No A is B.
Now, let's understand this from examples:
(1) Some Cakes are Roses
(2) All Roses are Trucks
(3) No Trucks are Bricks
(4) At least some Bricks are Hotels
(1) Some Trucks are Cakes
(2) Some Bricks are Roses
(3) All Cakes are Trucks
(4) Some Hotels are Cakes
Solution: First, you should draw basic diagrams.
Now, we can see that:
Conclusion1 is true. As Cakes and Trucks are intersecting each other.
Conclusion2: There is no relation mentioned between Bricks and Roses. So, we can’t comment about it.
Conclusion3: Intersection of Trucks and Cakes is due to Roses. We can’t comment about all Cakes.
Conclusion4: There is no relation mentioned between Hotels and Cars. So, we can’t comment about it.
Hence, Conclusion 1 follows.
Complementary Pairs: (Either & or) – Either and or cases only takes place in complementary pairs.
(i) Some A are B.
(ii) No A are B.
From the given above conclusions, it is easy to understand that one of the given conclusions must be true, which is represented by option either (i) or (ii). These types of pairs are called complementary pairs.
Note: ‘All A is B’ & ‘Some A is not B’ are also complementary pairs.
Note: It is important to note that, in complementary pairs, one of the two conclusions is true and others will be false simultaneously.
All A are B.
Some B is C.
I. All C is A.
II. Some C is not A.
Here we can make a conclusion, either I or either II follows.
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