## Navdeep Kaur is teaching live on Unacademy Plus

Syllogisms Basics, tips and tricks To solve all types of Questions For CBSE UGC NET and all Competitive Exams By Navdeep Kaur

Sets and Venn Diagrams Sets A set is a collection of things. . You write sets inside curly brackets like this: (socks, shoes, pants, watches, shirts, ...) You can also have sets of numbers: Set of whole numbers: (0, 1, 2, 3,...) Set of prime numbers: (2,3, 5,7, 11,13,17,...)

Let's take example: Ten Best Friends You could have a set made up of your ten best friends: (A, B, C, D, E, F, G, H, I, J) Each friend is an "element" (or "member") of the set. It is normal to use lowercase letters for them. Now let's say that a, c, d and h play Soccer: (It says the Set "Soccer" is made up of the elements a, c, d and Soccer = {A, C, D, H}

C, d and j play Tennis: Tennis = {C, D, J} We can put their names in two separate circles: Soccer A, C, D, H Tennis C, D, J

Union You can now list your friends that play Soccer OR Tennis. This is called a "Union" of sets and has the special symbol U: Soccer U Tennisfa, c, d, h, j) Not everyone is in that set.. only your friends that play Soccer or Tennis (or both). We can show that in a "Venn Diagram": Soccer Tennis A, H C,D

A Venn Diagram is clever because it shows lots of information: Do you see that a, c, d and h are in the "Soccer" set? And that c, d and j are in the "Tennis" set? And here is the clever thing: c and d are in BOTH sets! All that in one small diagram. Soccer Tennis A, H C,D

Intersection "Intersection" is when you must be in BOTH sets. In our case that means they play both Soccer AND Tennis which is C and D The special symbol for Intersection is an upside down "U" like this: n And this is how we write it down: Soccer n Tennis{c, d) Soccer C,D

Difference You can also "subtract" one set from another. For example, taking Soccer and subtracting Tennis means people that play Soccer but NOT Tennis .. which is A and H. And this is how we write it down: Soccer-Tennis = {A, H} Soccer Tennis Soccer A, H

Summary So Far . U is Union: is in either set n is Intersection: must be in both sets is Difference: in one set but not the other

Three Sets You can also use Venn Diagrams for 3 sets. Let us say the third set is "Volleyball", which D, G and J play: Volleyball = {D, G, J} But let's be more "mathematical" and use a Capital Letter for each set: S means the set of Soccer players T means the set of Tennis players V means the set of Volleyball players Tennis Soccer C A, H The Venn Diagram is now like this: D/ J Union of 3 Sets: S UTU V Volleybal

You can see (for example) that: Tennis D plays Soccer, Tennis and Volleyball J plays Tennis and Volleyball A and H play Soccer, but don't play Tennis or Volleyball no-one plays only Tennis Soccer C A, H D/ J Volleyball

Universal Set The Universal Set is the set that has everything. Well, not exactly everything. Everything that we are interested in now. Tennis Soccer C A, H D/ J In our case the Universal Set is our Ten Best Friends. Volleyball B, E, F, I U={A, B, C, D, E, F, G, H, I, J}

Thank you Rate and review the course Recommend the course to your friends https://unacademy.com/user/navclasses/

Given below is a diagram of three circles A, B & C inter-related with each of Indians. The circle B represents the class of scientists and circle C represents the class of politicians. p,q,r,s... represent different regions. Select the code containing the region that indicates the class of Indian scientists who are not politicians. (A) q and s only (B) s only (C) s and r only (D) p, q and s only Answer S

Which of the codes given below contains only the correct statements (a) Venn diagram represents the arguments graphically (b) Venn diagram can enhance our understanding (c) Venn diagram may be called valid or invalid (d) Venn diagram is clear method of notation (A) (a), (b) and (c) (B) (a), (b) and (d) (C) (b), (c) and (d) (D) (a), (c) and (d)

Select the code, which is not correct about Venn diagram: (A) Venn diagram represents propositions as well as classes. (B) It can provide clear method of notation. (C) It can be either valid or invalid. (D) It can provide the direct method of testing the validity Answer C

Study the following figure and answer the questions given below. How many doctors are neither artists nor players? 4 Artists Players Doctors 25 B. 5 C. 10 D. 30 8 30

Thank you Rate and review the course Recommend the course to your friends https://unacademy.com/user/navclasses/

The problems based on syllogism are on two parts: 1. Proposition/ Propositions 2. Conclusion/ Conclusions drawn from given proposition

Positive Negative Universal A All Cars are Rats E No Cars are Rats Particular l Some Cars are Rats O Some Cars are not Rats

2. NON-CATEGORICAL PROPOSITION It is different from categorical proposition which has condition attached with it. For example, "If M then P"

Rules- 1) If Statement is Positive then Conclusion must be Positive Example: Statement- All pens are pencils 2) If Statement is Negative then Conclusion must be Negative Example: Statement- No Pens are Pencils 3) +ve plus +ve = positive Conclusion +ve plus-ve = Negative Conclusion -ve plus-ve = No Conclusion eg. O+ O= No conclusion

Syllogisms Immediate and mediate Inferences For CBSE UGC NET and all Competitive Exams By Navdeep Kaur

-o

Mediate Inferences 1 Combine two Universal Positive statements will give Universal Positive Conclusion A+ A= A Statement: All Cars are Rats All Rats are Bats Conclusion: All Cars are Bats

2 Combine Universal Positive statement with Universal Negative will give Universal Negative Conclusion A+ E= E Statement: All Cars are Rats No Rats are Bats Conclusion: No Cars are Bats

Rules- 1) If Statement is Positive then Conclusion must be Positive Example: Statement- All pens are pencils For mediates: A+ A= A A+ E= E E + A= O Reverse E+1= 0 Reverse 2) If Statement is Negative then Conclusion must be Negative Example: Statement- No Pens are Pencils 3) +ve plus +ve = positive Conclusion +ve plus-ve = Negative Conclusion -ve plus -veNo Conclusion eg. O+ O= No conclusion

Steps: 1 Choose Statements If Subject and predicate are in one statements then - Immediate Inference If Subject and predicate are in Different statements then Mediate Inference 2 Check alignment: To merge Questions Common term should be predicate in first statement and Subject in Second statement in this case we change Order or Convert on the bases of IEA or Do Both as per situation

To merge Questions Common term should be predicate in first statement and Subject in Second statement in this case we change Order or Convert on the bases of IEA or Do Both as per situation Example: Statement: All Cars are Rats All Vans are Cars Conclusion: All Vans are Rats Au

Given below are two premises and four conclusions drawn from those premises. Select the code that expresses conclusion drawn validly from the premises (separately or jointly). Premises: (a) All dogs are mammals. (b) No cats are dogs. Conclusions: (i) No cats are mammals (ii) Some cats are mammals. (III) No Dogs are cats (iv) No dogs are non-mammals. Codes: (A) (i) only (B) (i) and (ii) (C) (iii) and (iv) (D) (ii) and (iii) No c nM

Thank you Rate and review the course Recommend the course to your friends https://unacademy.com/user/navclasses/

Square of Opposition Example if given is true then which of following is true

Contradictories: A and O E and I All Cars are Rats No Cars are Rats A and O Both cannot be true or false together means if one is false then other must be true Contradictories If A is true then O is false If O is true then A is false l Some Cars are RatsO Some Cars are not Should Have same Subject and Predicate Rats

Sub Altern Truth Downward but False Upward A All Cars are Rats E No Cars are Rats Sub Altern l Some Cars are RatsO Some Cars are not Rats

Sub Contraries land O Both can be true together but not false together Contraries A and E Both cannot be true together but can be false together A All Cars are E No Cars are Rats Rats A Contraries E | Subcontraries O Some Cars are Rats O Some Cars are not Rats