Syllogisms : Solved Examples

You may have some confusion regarding I and O types of statements. Each of the statements should be taken literally i.e. nothing should be assumed.
Let us take an example of a statement of type I.
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Some Ions are bars. This information just indicates that some part of the circle of Ions must be inside the circle of bars, may be all. Please note, the stated words are: may be. Therefore, this statement can be represented in three different diagrammatic ways, which are
All these three diagrams are valid ones. You should always make the first type of diagram, but always keep in mind that the second and third types of diagram are also possibilities. The second diagram indicates that, if you conclude that ‘Some Ions are not bars’, then it is incorrect. Now, if you choose the conclusion: ‘Some bars are not Ions’ from the third diagram, even that is wrong. Because the given statement is positive, you cannot conclude anything negative.
Let us try to find all the possible conclusions from the statements given. Let us take some examples.
Example 1: Statements:
I. Some pointers are schools.
II. Some schools are not casuals.
Sol : Now, in this case, the possible conclusion is Some schools are pointers (I to I)- the universal principle no. 4 states that with two particular statements only I to I is possible. Therefore, only 1 conclusion is possible.
Example 2: Statements:
I. Some horrors are not hens
II. Some tiles are not horrors.
Sol: It can be seen, that both the given statements are particular and none of the given statements is of type I, so no conclusion is possible.
Example 3 : Statements :
I. Some bricks are houses.
II. All houses are tanks.
Sol : Here the possible conclusions are
  1. Some houses are bricks. (I to I)
  2. Some tanks are houses. (A to I)
These conclusions have been derived from the individual statements alone, but if you combine these two statements, then the diagram will be as follows:
By combining these two statements, the third conclusion possible is ‘Some tanks are bricks’. Similarly the fourth conclusion is ‘some bricks are tanks’. So four conclusions are possible.
Example 4: Statements:
I. All X are Y.
II. All Y are Z.
Sol : Here by these statements, individually, the following conclusions can be drawn.
1. Some Y are X.
2. Some Z are Y.
Combining these two statements, we get the given diagram:
From this diagram, the conclusions, which can be drawn are
3. All X are Z.
4. Some Z are X.
Again, if you get the conclusion: 'Some Z are not X', then simply remember the universal principle no. 2, which states that with two positive statements, no negative conclusion is possible.
Example 5 : Statements:
I. All A are B
II. No B is C.
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Sol : Now individually, the conclusions are
1. Some B are A (A to I)
2. No C is B (E to E)
Again if you combine these two statements, then the diagram would be like
The conclusions, drawn from this diagram are
3. No A is C
4. No C is A.
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