# Shortcut to solve syllogism by rules

## Day 2 Topic: Reversal of Sentence (FIRST & LAST RULE)

(ii) Reversal of Proposition How to solve such statement? Here the common term is in the starting in both the proposition. For this we must know these four rules.

 Original Statement Reversed Statement All A is B Some B is A Some A is B Some B is A No A is B No B is A Some A is not B No Conclusion (Reversal Not Possible)

Let’s again take example 3:
Statement (a) Some A are B
(b) All A are C
Reverse statement (a) we get => Some B are A.
Now take the proposition in the order (a), (b) we get
Some B are A. All A are B [Now common entity are together.  So FIRST & LAST RULE is applicable.]

Doubt??????
In the above example, we reversed Some A are B. Can we reverse All A is C=> Some C are A????
Then arrange the proposition in the order (b), (a) ????
Some C are A + Some A are B. [Note here also FIRSt & LAST RULE is applicable.]
But which method is correct?? First , Second or Both????

To get the answer we will discuss the preference order for reversal rule

Preference Order for reversal of statement

The table below shows the order of preference for reversal.

 Order Relation Comments 1 Some, No Both Some and No have equal preference 2 All All has less preference than Some and No 3 Some Not Some Not cannot be reversed

Understand it by example.

Consider the following example:

(a) Some A are B
(b) No A are C
(c) All A are D
(d) All A are E

Example 1: Suppose we need to find relation between B and D. Then we need only proposition (a) and (c). But one of these must be reversed for FIRST & LAST RULE to be applicable.

According to above table Some has higher preference than All. So the statement with Some i.e proposition (a) must be reversed. We cannot reverse All here. So we get: Some B are A + All A are D

Example 2: Suppose we need to find relation between C and D. Then we need proposition (b) and (c) only. As per the table No has higher preference than All . So we have to reverse (b) we cannot reverse (c). So we will reverse proposition (b) and arrange in the order (b),(c) to get. No C is A + All A is C.

Example 3: Suppose we need to find relation between B and C. Then we need only proposition (a) and (b). Now Some and No both have equal preference. So we can reverse any one of them to get the desired result. i.e
Case 1: reverse (a) => Some B are A. and add it to (b)
Some B are A + No A is C
Case 2: reverse (b) => No C is A. and add it to (a)
No C is A + Some A are B

Example 4: Suppose we need to find relation between D and E. Then we need only proposition (c) and (d). here both the proposition contains ALL. So we can reverse either of them. Same as above.
Suppose we reverse (c) => Some D are A. + All A are E [FIRST & LAST RULE applicable now.]

So now our above discussed doubt has been cleared.

Practise sets for Reversal of Proposition

Example 1:
(a) Some A is B
(b) All C is B
(c) No D is A
Q1) Arrange the sentence to get a conclusion between D and B.
Solution 1) For B and C we have common term A in the proposition (a) and (c). Take them in order (c),(a) so that FIRST LAST RULE is applicable.
=> No D is A + Some A is B

Q2) Arrange the sentence to get relation between C and D.
Solution 2) Now we need to use both the rearrangement and reversal concept to achieve this goal. Follow this step:

(i) As per preference order we cannot Reverse statement (b) as it contains ALL. So fix statement as it is. (ii) Now the common entity between (b) and (a) is B. So reverse (a) so that FIRST LAST RULE is applicable.
We now have (b) + reverse(a) => All C is B + Some B is A.
(iii) Now the only proposition left is (c). The common entity between (a) and (c) is A. But for FIRST LAST RULE to be applicable (c) must be reverse.  So we have now
All C is B + Some B is A + No A is D.
(b) + reverse(a) + reverse(c)

Note: These are only for practice. When you get used to these concepts, you can simply solve the above questions in mind without using pen and paper. So practice these concepts regularly.

Example 2:
(a) All A is B
(b) No A is D
(c) All B is C

Q1) Arrange the above propositions to get a conclusion between D and C.

Steps:
(i) Note that here the highest preference is of proposition (b).On reversal it can be joined with (a) with the common entity A. So we have Reverse(a)+ (b)
(ii) Now the common entity between (a) and (c) i.e B, is already arranged. So we have: Reverse(a+(b)+ (c)

=> No D is A + All A is B + All B is C

## Exercise for the Day

Direction (1-3): Using the given statements answer the following questions:

(a) No C is B
(b) All A is B
(c) Some D is C

1. Arrange the propositions to get a conclusion between B and D

Explanation
: (c) + (a)=> Some D is C+ No C is B
2. Arrange the propositions to get a conclusion between A and C

Explanation
: (b) + reverse(a) =>All A is B + No B is C
3. Arrange the propositions to get a conclusion between A and D

Explanation
: (b) + rev(a)+rev(c) =>All A is B + No B is C + Some C is D

Direction (4-5): Using the given statements answer the following questions:

(a) All A is B
(b) No C is B
(c) All A is D

1. Arrange the propositions to get a conclusion between A and C

Explanation
: (a) + reverse(b)
2. Arrange the propositions to get a conclusion between D and C

Explanation
: reverse(c) + (a) + reverse(b)

The real Syllogism will start from tomorrow. Don’t miss any day.