Syllogism — RRB NTPC General Intelligence & Reasoning

• Given: Statements: Some keys are chess. All chess are locks. No lock is a rock.

• Solution:
Step 1: Draw a circle for keys. Overlap it with a circle for chess (Some keys are chess).
Step 2: Draw a larger circle representing locks that completely encloses the chess circle (All chess are locks).
Step 3: Draw a separate circle for rocks and put a cross between the locks circle and the rocks circle (No lock is a rock).
Step 4: Evaluate Conclusion I: Some keys are locks. The part of the keys circle that overlaps with the chess circle is entirely within the locks circle. Therefore, some keys are indeed locks. Conclusion I is true.
Step 5: Evaluate Conclusion II: No chess is a rock. Since all chess are inside locks, and no lock is a rock, it's impossible for any chess to be a rock. Therefore, no chess is a rock. Conclusion II is true.

• Exam Trick: When 'All A are B' and 'No B is C', then 'No A is C' is always true. Since all chess are locks and no lock is a rock, no chess is a rock.

• Final Answer: Both conclusions I and II follow

• Given: Statements: Some phones are laptops. All laptops are computers. No computer is a tablet.

• Solution:
Step 1: Draw circles for phones and laptops, intersecting them.
Step 2: Draw a larger circle for computers enclosing the laptops circle entirely.
Step 3: Draw a separate circle for tablets and put a cross between computers and tablets.
Step 4: Eval I: The intersection of phones and laptops is inside computers. So, some phones are computers is true.
Step 5: Eval II: All laptops are inside computers, and computers have a strict 'no' relationship with tablets. Thus, no laptop is a tablet is true.
Step 6: Eval III: Tablets have a 'no' relationship with computers (and laptops inside). However, there's no direct negative relationship given between tablets and the part of phones outside the computer circle. We cannot definitely say 'some tablets are not phones'. It's a possibility, but not a certainty. Therefore, III is false.

• Exam Trick: Negative conclusions without a direct cross connection in the statements are usually false in surety cases. Here, no direct cross exists between tablets and the whole of phones.

• Final Answer: Only conclusions I and II follow

• Given: Statements: No tree is a flower. Some flowers are leaves. All leaves are green.

• Solution:
Step 1: Draw a circle for trees and a separate circle for flowers, putting a cross between them.
Step 2: Draw a circle for leaves intersecting with the flowers circle.
Step 3: Draw a larger circle for green enclosing the entire leaves circle.
Step 4: Eval I: The part of leaves that are flowers is also part of 'green' (since all leaves are green). These specific 'green' things (which are also flowers) cannot be trees because no flower is a tree. Therefore, 'Some green things are not trees' is true.
Step 5: Eval II: There is a cross between trees and flowers. The part of leaves that is inside flowers cannot be trees. But what about the part of leaves outside the flowers circle? We don't have definite information about that part's relationship with trees. It might or might not be trees. Thus, we cannot definitely say 'No leaf is a tree'. Conclusion II is false.

• Exam Trick: Find the hidden connection. Some green things are flowers, and no flowers are trees. Therefore, some green things (the flower part) are not trees.

• Final Answer: Only conclusion I follows

• Given: Statements: Some apples are bananas. Some bananas are cherries.

• Solution:
Step 1: Draw circles for apples, bananas, and cherries. Apples intersect with bananas, and bananas intersect with cherries.
Step 2: Note that there's no definite information given about the relationship between apples and cherries. They might intersect, or they might not.
Step 3: Eval I: Some apples are cherries. We cannot say this for sure. False.
Step 4: Eval II: No apple is a cherry. We also cannot say this for sure. False.
Step 5: Both conclusions are individually false. They share the same subjects and predicates (apples, cherries). One is positive ('Some') and the other is negative ('No'). This forms a complementary pair.
Step 6: Therefore, the 'Either-Or' condition is satisfied.

• Exam Trick: When checking for Either-Or, ensure both conclusions are false, have the same parameters, and form a positive-negative pair like Some/No or All/Some Not. Here, Some/No fits perfectly.

• Final Answer: Either conclusion I or II follows

• Given: Statements: All dogs are cats. All cats are rats.

• Solution:
Step 1: Draw a circle for dogs enclosed completely within a circle for cats. Enclose the cats circle completely within a circle for rats.
Step 2: Eval I: All rats are dogs. Looking at the diagram, while all dogs are inside the rats circle, it's not necessarily true that the entire rats circle is filled by dogs. Thus, we cannot definitely say all rats are dogs. False.
Step 3: Eval II: Some rats are not dogs. While it looks like there's empty space in the rats circle outside dogs, it's a possibility that the circles overlap perfectly (i.e., Dogs = Cats = Rats). Since we can't rule out that possibility, we cannot definitely state that some rats are not dogs. False.
Step 4: Both conclusions are false. They have the same parameters (rats, dogs). One is positive ('All') and the other is negative ('Some not'). They form a complementary pair.
Step 5: Thus, either I or II must be true.

• Exam Trick: Remember the complementary pairs for Either-Or: Some/No, and All/Some Not. Ensure both conclusions are individually false before applying this rule.

• Final Answer: Either conclusion I or II follows

• Given: Statements: Some pins are needles. Some needles are threads. No thread is a cloth.

• Solution:
Step 1: Draw circles for pins, needles, and threads overlapping sequentially. Put a cross between threads and clothes.
Step 2: Eval I: Some pins are threads. No direct connection is shown between pins and threads. It's a possibility, but not a certainty. False.
Step 3: Eval II: No pin is a thread. There's no direct negative connection shown. It's a possibility, but not a certainty. False.
Step 4: Check for Either-Or between I and II. Both are false, same parameters (pins, threads), one is 'Some', the other is 'No'. They form a complementary pair. So, Either I or II follows.
Step 5: Eval III: Some needles are not cloths. The part of needles that overlaps with threads cannot be clothes (because no thread is a cloth). Thus, this specific part of needles is not clothes. Conclusion III is definitely true.
Step 6: Combining results, we get Either I or II follows, and III follows.

• Exam Trick: Always check false conclusions with identical parameters for Either-Or conditions before finalizing your answer. The intersection of 'needles' and 'threads' proves 'some needles are not cloths'.

• Final Answer: Either conclusion I or II follows, and conclusion III follows

• Given: Statements: Some laptops are computers. No computer is a mobile.

• Solution:
Step 1: Draw circles for laptops and computers intersecting. Put a cross between computers and mobiles.
Step 2: Eval II: Some laptops are not mobiles. The part of laptops that intersects with computers cannot be mobiles because no computer is a mobile. Thus, this specific part of laptops is definitely not mobiles. Conclusion II is true.
Step 3: Eval I: All laptops being mobiles is a possibility. Since we established in Step 2 that a part of laptops (the part overlapping with computers) can never be mobiles, it is impossible for all laptops to be mobiles. This possibility contradicts the statements. Thus, Conclusion I is false.

• Exam Trick: If 'Some A are not B' is definitely true, then 'All A can be B' is always false as a possibility because the part that is not B prevents the whole from being B.

• Final Answer: Only conclusion II follows

• Given: Statements: All papers are books. Some books are pens.

• Solution:
Step 1: Draw circles: papers inside books, and books intersecting with pens.
Step 2: Note that there's no definite information connecting papers and pens directly. They might intersect, one might be inside the other, or they might be completely separate, as long as all papers are in books and some books are in pens.
Step 3: Eval I: All pens being papers is a possibility. Since there are no negative statements restricting pens from being inside papers, this is a valid possibility. We could draw the 'pens' circle entirely inside the 'papers' circle while still satisfying 'some books are pens'. Conclusion I is true.
Step 4: Eval II: Some papers being pens is a possibility. Similarly, we could draw the circles such that they intersect, satisfying all conditions. Conclusion II is true.

• Exam Trick: When no direct relationship (positive or negative) is given between two parameters, almost any possibility between them is considered true, provided it doesn't contradict the given statements.

• Final Answer: Both conclusions I and II follow

• Given: Statements: No red is yellow. No yellow is green.

• Solution:
Step 1: Draw circles for red, yellow, and green. Put crosses between red & yellow, and yellow & green.
Step 2: Note there's no direct info between red and green.
Step 3: Eval I: Some red are green. No definite proof. False.
Step 4: Eval II: No red is green. No definite proof. False.
Step 5: Check Either-Or for I and II. Both false, same parameters (red, green), positive ('Some') and negative ('No') pair. Therefore, Either I or II follows.
Step 6: Eval III: All red being green is a possibility. Since there's no negative statement linking red and green directly, they could entirely overlap without violating the conditions (red and green could be the same circle, both having a 'no' relationship with yellow). This is a valid possibility. True.

• Exam Trick: Don't assume transitive negative relationships. 'A is not B' and 'B is not C' does NOT mean 'A is not C'. A and C could be anything to each other, so possibilities between them are true.

• Final Answer: Either conclusion I or II follows, and conclusion III follows

• Given: Statements: All boys are men. Some men are doctors.

• Solution:
Step 1: Draw boys circle inside men circle. Draw doctors circle intersecting men circle.
Step 2: Eval I: All boys can never be doctors. 'Can never be' is equivalent to a definite 'are not'. Are all boys definitely not doctors? No. There is no negative statement preventing the boys circle from being entirely inside the doctors circle (while still being inside men). So, it's possible they can be. Thus, 'can never be' is false.
Step 3: Eval II: Some boys being doctors is a possibility. As established, boys and doctors have no direct negative constraint. They could overlap. This possibility is true.

• Exam Trick: Treat 'can never be' as a strict 'are definitely not'. If you can draw a valid diagram where they are, then the 'can never be' statement is false.

• Final Answer: Only conclusion II follows