SELECTIVE APPROACH TO SOLVING SYLLOGISM


 Diana Wilkerson
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1 SELECTIVE APPROACH TO SOLVING SYLLOGISM While solving Syllogism questions, we encounter many weird Statements: Some Cows are Ugly, Some Lions are Vegetarian, Some Cats are not Dogs, Some Girls are Boys, and such. The people who are comfortable using Venn Diagrams waste not a second more making the quickest Diagram based upon the given Statements. Ironically, this is not the case for others. Some find these questions challenging, cumbersome and time consuming to the point that they skip these at the first sight. But worry not. Syllogism is a piece of cake! I ll show you how. Give me about 20 minutes. Diagram Selection The basic thing to remember about Syllogism is: One Statement tells many things and thus, many Diagrams are possible. For example, consider this basic Statement: Some A are not B. Now, according to this Statement, three Diagrams are possible. These are shown here. (1) (2) (3) 1st Diagram is similar to basic Diagram of Some A are B. 2nd Diagram is similar to basic Diagram of No A are B. 3rd Diagram is similar to basic Diagram of All B are A. But which Diagram to select for solving question? 1st or 2nd or 3rd? Confused?? Well, don t be. Pay attention now. Selection of the best Diagram follows a very simple concept. And that is: Circles in Diagram should Overlap as Minimum as Possible
2 Why Minimum? For the very basic reason: Minimum is the overlap, minimum will be the confusion. So, 1st, 2nd or 3rd, which Diagram is the best to select? Answer is: 2nd one!! Okay! There are three more basic Statements. Some A are B. All A are B. No A are B. For these Statements as well, we ll select the Diagram in which minimum overlap of the circle is there. Minimum Overlap Diagrams for these Statements are given here. Some A are B All A are B No A are B Note three things here. Making Diagrams Quickly 1. The Diagram of Some A are B is drawn as such. 2. In Diagram of All A are B, I ve touched the boundaries of circle A and B. This results in further minimization of overlap (I ll show you how). 3. In Diagram of No A are B, I ve drawn a line with cross between circles A and B. This way I pretty much remembers their relation without confusion. Now let s shed some more light upon Point no. 2 mentioned above. Let we have few Statements as: A. Some Headphones are Earphones. B. All Earphones are Telephones.
3 Now, I m making three different Diagrams based upon these two Statements. (1) (2) (3) Tell me which Diagram has the Minimum Overlap? 1st, 2nd or 3rd? Of course, the 2nd one!! This boundary touching approach further reduces the overlap of a combination of Statements, like: A. All Comedians are Funny. B. All Comedians are Actors. Notice the way Red portion didn t come in circles drawn by hand. A. Some Pots are Keys. B. Some Keys are Locks. C. All Keys are Rings. Notice the way I didn t overlap the P and L circles. A. All Employees are Owners. B. No Owner is a Wager. C. Some Employees are not Managers. D. All Managers are Gatekeepers. E. Some Wagers are Managers. Notice the way I ve drawn the E and M circles That s how we draw the Diagrams so that Circles should have a Minimum Overlap. Pick up a few Syllogism Statements and practice these Diagram making approaches.
4 Applying These Approaches One more thing remains, which is necessary to learn before you embark upon solving Syllogism questions. And that is: Checking the validity of Conclusions. Let s learn this as we go along solving this interesting example. Statements: Question 1 A. Some Banks are Shops. B. Some Shops are Markets. C. All Markets are Junk. I. Some Junk are Shops. II. Some Markets are Banks. III. No junk is a Bank. IV. No Junk being Banks is a possibility. The Best Diagram (Minimum Overlap) is shown here. Now pay attention! To check the validity of a Simple Conclusion (no Possibility), just try to refute (prove false) the Conclusion. This is how it is done. 1. See Conclusion I Some Junk are Shops. To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says Some Junk are Shops. If we can prove No Junk are Shop is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is No Junk are Shop possible? The Minimum Overlap Diagram says it s not possible. We cannot prove this Conclusion false. So, this Conclusion will follow in ALL THE CASES.
5 2. See Conclusion II Some Markets are Banks To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says Some Markets are Banks. If we can prove No Market are Bank is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is No Market are Bank possible? The Minimum Overlap Diagram says it s possible. So, if No Market are Bank is possible, Some Markets are Banks will not follow. As simple as that. (You see, Minimum Overlap Diagram reduces so much work while checking the validity of the questions.) 3. See Conclusion III No Junk is a Bank. To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says No Junk is a Bank. If we can prove that Some Junk are Bank is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is Some Junk are Bank possible? Yes, it is possible. See the Diagram (Here, another Diagram is shown, but you can easily imagine this Diagram all in your head.) So, if Some Junk are Bank is possible, No Junk is a Bank will not follow. As simple as that. Now pay attention again! Validity checking of Possibility Conclusions runs different course. We tried to prove false the Simple Conclusions, but when it comes to Possibility Conclusions, we try to prove them true. 4. See Conclusion IV No Junk being Bank is a Possibility To check whether this Conclusion follows or not, we ll try to prove this Conclusion true. Conclusion asks, is No Junk are Bank Possible? Of course, it is possible.
6 Some Junk are Bank is possible and No Junk are Bank is also possible. So, this Conclusion follows. And doing all this, we ve solved this question. Full marks! You don t even have to remember this table to check the validity of Simple Conclusions. (If CounterConclusion is possible, Simple Conclusion will not follow.) Conclusion CounterConclusion 1. Some A are B No A are B 2. No A are B Some A are B 3. All A are B Some A are not B 4. Some A are not B All A are B Just note: 1. The CounterConclusion of Some A are B is No A are B while the CounterConclusion of No A are B is Some A are B. These are CounterPairs. 2. The CounterConclusion of All A are B is Some A are not B while the CounterConclusion of Some A are not B is All A are B. These are also CounterPairs. With practice only you ll learn that you don t need to counter check the Conclusion every time. Minimum Overlap Diagram does much of the work for you. Why? Because you cannot go more Minimum than that! Let s quickly solve some of the questions now. Statements: A. Some Questions are Answers. B. All Questions are Puzzles. C. No Puzzle is Problem. I. Some Puzzles are Answers. II. No Question is a Problem. Conclusion I? Follows! Conclusion II? Follows! Question 2
7 Question 3 Same Statements as of Question 2 I. All Problem being Answer is a Possibility. II. All Problem being Question is a Possibility. Conclusion I? Follows! Conclusion II? Doesn t Follows! Statements: A. No Second is Hour. B. Some Minutes are Time. C. All Hours are Minutes. Question 4 I. All Hours are Time. II. Some Minutes being Second is a Possibility. Conclusion I? Doesn t Follows! Conclusion II? Follows! (Just imagine) And that s all what is needed to solve Syllogism the quickest way! Practice as much as you can until you feel comfortable solving the questions using these methods. Thank You! All the very best!!
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