Syllogism by Rules Part 1 : Arrangement of Sentence

Shortcut to solve syllogism by rules

Day 1 Topic: Arrangement of Sentence (FIRST & LAST RULE)

Today we will discuss the basic methods that will help us in solving syllogisms in a fast and effective manner. The real rules will start from Day 3. But without the knowledge of the concepts that we will discuss today, you cannot move on to rules directly. So understand these concepts well.

Basic Terms used in syllogism that we will follow in our post

Sample example of sentence in Syllogism: Some A are B

  • Entity/Term: The terms between which relation is given is referred as entity. Here A and B are entity.
  • Relation: Some, All, No, Some Not are examples of relation.
  • Proposition/Sentence: The statement from which we have to derive the conclusion. We can refer to it by statement also in general.
  • Conclusion: The derived solution from the proposition.

The main concept of Syllogism: FIRST AND LAST RULE

Our main aim in syllogism is to arrange the given proposition in such a way that the entities which are common in the multiple propositions always come together. Let’s understand it by an example.

Example: Consider these three statements:

But this may not be the case always. Some time in question, we may get propositions which are not arranged. We have to manually arrange them and then start solving the question. So we will use the FIST AND LAST RULE as our starting step in solving syllogism.

FIRST & LAST RULE: The propositions should be arranged in such a manner that, the two entities between which the conclusion is to be found out should come at the beginning and at the last while the common term should be in middle. i.e One should be come at the beginning and the other should be at the last.

Example: In the above example 1: The entity at the beginning is A and at the last is D. So using these three statements together we can find the relation between A and D.
If we consider only statements b) and c) then the first entity is B and Last entity is D. So using these two propositions we can find the relation between B and D.
If we consider only statement a) and b) then the FIRST entity is A and the last entity is B, so using these two together we can find the relation between A and B.

We must note that in Example 1, the propositions are already arranged in the desired manner. But in reality it may not be arranged. We have to arrange them by using certain methods. We will discuss two methods to achieve this.

(i) Rearrangement of Proposition – Day 1
(ii) Reversal of Proposition – Day 2

(i) Rearrangement of Proposition

First identify the common terms. And arrange them accordingly. With non-common entity at FIRST and LAST and the common entity coming together as shown in example 1 (b) highlighted entity B,B and C,C comes together. Example:

Now if we want to find relation between G and C, we will use just proposition (a) and (b)
If we want to find relation between F and Z, we will use the proposition (c) and (a)
For relation between F and C we will use all (c), (a) and (b).

For concept of rearrangement to work, one of the common entity should be at the last of the proposition and the other should be starting.

Example: All A are B. Some B are C. Here the common entity is B. It comes at the end in proposition 1 while at the start in Proposition 2.
Example: All A are B. Some A are C. Here the common term is A. But in both the proposition A is at the beginning. So in such case we cannot use the concept of rearrangement. The method to solve such a case will be discussed later.

More Examples:

Exercise 1) Arrange these propositions in such a way that common entity comes together:

(a) No tiger is lion
(b) Some elephant are tiger
(c) All lion are monkey

Solution: The common terms are tiger and lion. Arrangement is (b),(a),(c) i.e
Some elephant are tiger. No tiger is lion. All lion are monkey.

Exercise 2) Arrange these propositions in such a way that common entity comes together:

(a) Some red are blue
(b) All black are pink
(c) some blue are black
(d) No pink is violet

Solution:  (a),(c),(b),(d)
so we have now
(a) Some red are blue
(c) some blue are black
(b) All black are pink
(d) No pink is violet

Ques) Which propositions are required to get a relation between blue and violet.
Answer: (c),(b),(d) [FIRST and LAST RULE] – The two entity between which relation is to be found out should come at beginning and at last.

Ques) Which propositions are required to get a relation between red and pink.
Answer: (a),(c),(b) [FIRST and LAST RULE

LIMITATION of REARRANGEMENT

Consider this example:

We will discuss the solution to this problem on Day 2.

Exercise for the Day

Q1) Arrange the given statement according to the FIRST & LAST rule to find a relation between CONE and RECTANGLE.
(a) All cones are cylinders.
(b) No square is a rectangle.
(c) All cylinders are squares.

View Answer
Correct Order is: (a)(c)(b)
Explanation
: As we have to find relation between CONE and RECTANLGE, they should come at the beginning and at the end. So start with the statement that has CONE in the start. i.e (a).  Now the common term cylinder is in (a) and (c). So next proposition is (c) followed by (b).

Q2) Arrange the given statement according to the FIRST & LAST rule to find a relation between GRAPE and SWEET
(a) No orange is apple.
(b) All grapes are oranges.
(c) Some apples are sweet.

View Answer
(b) (a) (c)

Q3) Arrange the given statement according to the FIRST & LAST rule to find a relation between PRETTY and BOYS

(a) All girls are pretty.
(b) Some smart are girls.
(c) Some boys are smart.

View Answer
(c) (b) (a)
Explanation
: Start with the proposition which has either BOY or PRETTY in it. We have (c) and (a) . But choose (c) because it has boy in the starting. It will be easy. While (a) has PRETTY at the end. (c) follow by (b) [due to common term smart] followed by (a) [] due to common term girls

Q4) Arrange the given statement according to the FIRST & LAST rule to find a relation between BUSSES and PLANE

(a) No plane is metro
(b) All busses are rails.
(c) Some rail is plane.

View Answer
(b) (c)
Explanation
: Start with (b) it has BUSSES in starting. Common term rails is in (b) (c) SO we now have BUSSES and PLANE in starting and end. So FIRST LAST RULE is satisfied.

Q5) Arrange the given statement according to the FIRST & LAST rule to find a relation between SILVER and PLATINUM

(a) No gold is silver.
(b) Some platinum is gold.
(c) Some silver are diamond.

View Answer
(b) (a) 

We will discuss Reversal of Preposition on Day 2.  

Ask your doubt in comment section.

Thank You!!!!!

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55 Thoughts to “Syllogism by Rules Part 1 : Arrangement of Sentence”

  1. K!nG Iz B!nG

    Again gr8 initiative by shubra mam,,,,
    Ty fr ur support:)

  2. Destiny : ultimate

    Thank you sir 🙂

  3. •?((¯°·._.• ąʍβɨЌą •._.·°¯))؟•

    thanku so much sir :))

  4. ANUP SINGH

    ty sir 🙂

  5. MiMi

    thank u suraj sir

  6. Yogi ji

    In Exam main only ek hi option diya hta hai. Wha ye rule Kaise kaam aayega

  7. Yogi ji

    Exam main Kaise karege is rule se venn Diagram phir bhi banana padhga

    1. James Bond 007

      Jisse comfortable ho usi se karo

      1. Yogi ji

        Ryt bro. Main soch rha ki ye rule main Bola kya gya hai.

    2. Suraj

      Read the first paragraph :
      Today we will discuss the basic methods that will help us in solving syllogisms in a fast and effective manner. The real rules will start from Day 3. But without the knowledge of the concepts that we will discuss today, you cannot move on to rules directly. So understand these concepts well.

      So jaise jaise post ho rhi hai,, un posts ko samjho,, and till day 3 sab clear ho jayega.. and till day 6 sare cheeze aa jayegi.. abhi aage ka mat socho

      1. James Bond 007

        Hmm GA

      2. Yogi ji

        Ye bol rha ki is rule main kya Bola gya

        1. Suraj

          ye bola gaya hai ki kis tarah se sentences ko arrange karna hai taki conclsuion mile

        2. Suraj

          nhi samjh aaye to u can continue with venn

  8. James Bond 007

    Suraj der

      1. James Bond 007

        Ek quant questions solve kr

      1. James Bond 007

        Pata nai solution daal

      2. James Bond 007

        a) 26th day
        b)27the day
        c)28th day
        d)30th day

        1. Suraj

          ha ruko ,, kuch gadbad kar diya

          1. James Bond 007

            1hr le le

          2. Suraj

            600 ko 45 se divide karo,, 13 something ayega… to bas 13 lo…

          3. Yogi ji

            Phir double krna 26 aayega

        2. Suraj

          b) 27 days
          work completed on first day by A and B= 6/240 + 4/300
          on second day = 4/240 + 6/300

          means total work completed in 2 days =1/40 + 1/75 + 1/60 + 1/50 = 45/600
          this pattern will repeat
          means in 26 days 45*13=585/600 work is completed
          means reamining work = 15/600=3/120
          now ab A ki bari hai work karne ki he can do this work in 3/120 *240/6 = 1 means in his complete time i.e 6 hours
          so total day = 26+1 =27 days

          1. James Bond 007

            Hmm *10hr consider nai kiya tha Maine first time got

    1. Laughing tym its nitrous oxide

      240…………….300
      …………1200
      5………………4
      A…….5*6=30
      B===4*4==16………..
      B===4*6=24
      A===5*4=20
      30+16+24+20==90 WORK IN TWO DAY
      90*13===1170
      13*2=26 DAY 6 HRS

      1. James Bond 007

        a= 240 hr , b= 300 hr  
        tw= 1200
        a= 5
        b= 4 
        1st day = 5*6 + 4*4 = 46 
        2 nd day= 5*4 + 4*6 = 44 
        in 2 day = 90 unit  
        2*13 = 90*13 
        in 26 th day = 1170unit  
        so rest in 27th day..

        1. Laughing tym its nitrous oxide

          YUP 16 JI JAGAH 6 LE LIYA :p TOTAL TABHI 80 AYA

          1. James Bond 007

            🙂

          2. Laughing tym its nitrous oxide

            26 DAY 6 HRS AYEGA MAY BE

          1. James Bond 007

            Total 1200 unit hai na to aisa multiple dhundo Jo iske equal ho ya kam

          2. Yogi ji

            Read the following information carefully and answer the questions given below it:
            Out of the total number of 7800 girls in a college, 15% are good at dancing and 20% of the number of girls good at dancing are also good in studies. 5% of the total number of girls in the college are good at drawing and 10% of the girls good at drawing are also good in studies. 35% of the total number of girls in the college are good at cooking and 20% of the girls good at cooking are also good in studies; also, 30% of the girls good at cooking are good at dancing but not good in studies. 10% of the total number of girls in the college are good only at singing. 25% of the total number of girls in the college are good at sports and 16% of the number of girls good at sports are also good at studies. Rest of the girls from the college are only good at studies..

  9. Yogi ji

    All a is B. All a is c
    Conclusions =all C is B?

      1. Yogi ji

        If possiblty hti to

        1. Suraj

          tab true hota…

          1. Yogi ji

            Some bhi false hota na

          2. Suraj

            some b is c ya some c is b true hota

          3. PHENOMENAL

            Thanx sir

    1. Yogi ji

      All B is c bhi false?

        1. Yogi ji

          Read the following information carefully and answer the questions given below it:
          Out of the total number of 7800 girls in a college, 15% are good at dancing and 20% of the number of girls good at dancing are also good in studies. 5% of the total number of girls in the college are good at drawing and 10% of the girls good at drawing are also good in studies. 35% of the total number of girls in the college are good at cooking and 20% of the girls good at cooking are also good in studies; also, 30% of the girls good at cooking are good at dancing but not good in studies. 10% of the total number of girls in the college are good only at singing. 25% of the total number of girls in the college are good at sports and 16% of the number of girls good at sports are also good at studies. Rest of the girls from the college are only good at studies.

        2. Yogi ji

          Kaise krna ye total main se total nikalna

    2. Raviraj Sontakke

      Some B are c

  10. purvi

    thanku sir 🙂

  11. MAYANK BHARADWAJ100%

    thks

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