Episode 8 — Aptitude and Reasoning / 8.22 — Syllogism

8.22 Practice MCQs -- Syllogism

Instructions: For each question, determine which conclusion(s) logically follow from the given statements. Treat all statements as TRUE even if they seem to contradict common knowledge. Answers and explanations are at the end.

Q1.

Statements: All cats are dogs. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats.

(a) Only I follows
(b) Only II follows
(c) Both I and II follow
(d) Neither follows

Q2.

Statements: No tree is a flower. All flowers are fruits. Conclusions: I. No tree is a fruit. II. Some fruits are not trees.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q3.

Statements: Some pens are pencils. Some pencils are books. Conclusions: I. Some pens are books. II. No pen is a book.

(a) Only I follows
(b) Only II follows
(c) Either I or II follows
(d) Neither follows

Q4.

Statements: All students are scholars. No scholar is lazy. Conclusions: I. No student is lazy. II. Some scholars are students.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q5.

Statements: Some apples are oranges. All oranges are mangoes. Conclusions: I. Some apples are mangoes. II. All mangoes are oranges.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q6.

Statements: All cars are buses. Some buses are trains. Conclusions: I. Some cars are trains. II. Some trains are buses.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q7.

Statements: No man is a boy. No boy is a girl. Conclusions: I. No man is a girl. II. Some girls are not men.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q8.

Statements: All A are B. Some B are C. No C is D. Conclusions: I. Some B are not D. II. Some A are C.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q9.

Statements: Some kings are queens. All queens are princesses. Conclusions: I. Some kings are princesses. II. All princesses are queens.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q10.

Statements: All roses are red. All red things are beautiful. Conclusions: I. All roses are beautiful. II. Some beautiful things are red.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q11.

Statements: No chair is a table. All tables are wood. Conclusions: I. No chair is wood. II. Some wood is not chair.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q12.

Statements: Some M are N. All N are O. Some O are P. Conclusions: I. Some M are O. II. Some M are P.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q13.

Statements: All doctors are engineers. Some engineers are teachers. Conclusions: I. Some doctors are teachers. II. All teachers are doctors.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q14.

Statements: No X is Y. Some Y are Z. Conclusions: I. Some Z are not X. II. No X is Z.

(a) Only I follows
(b) Only II follows
(c) Either I or II follows
(d) Both follow

Q15.

Statements: All rivers are lakes. No lake is an ocean. Conclusions: I. No river is an ocean. II. Some oceans are rivers.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q16.

Statements: Some rich are poor. Some poor are honest. Conclusions: I. Some rich are honest. II. No rich is honest.

(a) Only I follows
(b) Only II follows
(c) Either I or II follows
(d) Neither follows

Q17.

Statements: All cups are saucers. All saucers are plates. All plates are bowls. Conclusions: I. All cups are bowls. II. All saucers are bowls. III. Some bowls are cups.

(a) I and II follow
(b) II and III follow
(c) I and III follow
(d) All follow

Q18.

Statements: Some birds can swim. All things that swim are fish. Conclusions: I. Some birds are fish. II. All fish are birds.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q19.

Statements: All politicians are honest. No honest person is corrupt. Conclusions: I. No politician is corrupt. II. Some honest persons are politicians.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q20.

Statements: Some books are pens. All pens are erasers. No eraser is a sharpener. Conclusions: I. Some books are erasers. II. No pen is a sharpener. III. Some books are not sharpeners.

(a) I and II follow
(b) II and III follow
(c) I and III follow
(d) All follow

Q21.

Statements: All singers are dancers. No dancer is a painter. Conclusions: I. No singer is a painter. II. Some painters are singers.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q22.

Statements: Some phones are laptops. Some laptops are tablets. Conclusions: I. All phones are tablets. II. Some phones are not tablets.

(a) Only I follows
(b) Only II follows
(c) Either I or II follows
(d) Neither follows

Q23.

Statements: All X are Y. No Y is Z. Some Z are W. Conclusions: I. No X is Z. II. Some W are not Y. III. Some W are Z.

(a) I and III follow
(b) I and II follow
(c) All follow
(d) Only I follows

Q24.

Statements: Some girls are beautiful. All beautiful things are natural. Conclusions: I. Some girls are natural. II. All natural things are beautiful.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q25.

Statements: No A is B. All B are C. Conclusions: I. Some C are not A. II. No A is C.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q26.

Statements: All mountains are tall. Some tall things are rivers. All rivers are deep. Conclusions: I. Some tall things are deep. II. Some mountains are deep.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q27.

Statements: Some red are blue. Some blue are green. Conclusions: I. Some red are green. II. Some green are blue.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q28.

Statements: All P are Q. All Q are R. Some R are S. Conclusions: I. All P are R. II. Some P are S.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q29.

Statements: No sun is a moon. All moons are stars. Conclusions: I. No sun is a star. II. Some stars are moons.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q30.

Statements: Some poets are writers. All writers are artists. No artist is a scientist. Conclusions: I. Some poets are artists. II. No writer is a scientist. III. Some poets are not scientists.

(a) I and II follow
(b) I and III follow
(c) II and III follow
(d) All follow

Q31.

Statements: All balls are round. All round things are spheres. No sphere is flat. Conclusions: I. No ball is flat. II. All balls are spheres.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q32.

Statements: Some keys are locks. No lock is a door. Conclusions: I. Some keys are not doors. II. All keys are doors.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q33.

Statements: All tigers are animals. Some animals are dangerous. Conclusions: I. Some tigers are dangerous. II. All dangerous things are animals.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q34.

Statements: Some sweet things are sour. All sour things are bitter. Conclusions: I. Some sweet things are bitter. II. Some bitter things are sweet.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q35.

Statements: All diamonds are gems. All gems are stones. No stone is metal. Conclusions: I. No diamond is metal. II. All diamonds are stones. III. Some stones are gems.

(a) I and II follow
(b) II and III follow
(c) I and III follow
(d) All follow

Q36.

Statements: No fish is a bird. Some birds are black. Conclusions: I. Some black things are not fish. II. No fish is black.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q37.

Statements: All tea is coffee. No coffee is milk. Conclusions: I. No tea is milk. II. Some coffee is tea.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q38.

Statements: Some teachers are kind. All kind people are loved. Conclusions: I. Some teachers are loved. II. All loved people are kind.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q39.

Statements: All elephants are big. Some big things are grey. No grey thing is white. Conclusions: I. Some elephants are grey. II. Some big things are not white.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q40.

Statements: Some A are B. All B are C. Conclusions: I. All A are C. II. Some A are not C.

(a) Only I follows
(b) Only II follows
(c) Either I or II follows
(d) Neither follows

Q41.

Statements: All squares are rectangles. All rectangles are parallelograms. Some parallelograms are rhombuses. Conclusions: I. All squares are parallelograms. II. Some squares are rhombuses.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q42.

Statements: No computer is a phone. All phones are smart. Conclusions: I. No computer is smart. II. Some smart things are not computers.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q43.

Statements: All medicines are drugs. Some drugs are chemicals. All chemicals are harmful. Conclusions: I. Some drugs are harmful. II. Some medicines are harmful.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q44.

Statements: Some actors are singers. Some singers are dancers. All dancers are artists. Conclusions: I. Some singers are artists. II. Some actors are artists.

(a) Only I follows
(b) Only II follows
(c) Both follow
(d) Neither follows

Q45.

Statements: All roses are jasmine. No jasmine is lily. Some lilies are lotus. Conclusions: I. No rose is lily. II. Some lotus are not jasmine. III. Some jasmine are roses.

(a) Only I follows
(b) I and III follow
(c) Only III follows
(d) All follow

Answer Key

QAnsQAnsQAnsQAnsQAns
1(c)10(c)19(c)28(a)37(c)
2(b)11(b)20(d)29(b)38(a)
3(c)12(a)21(a)30(d)39(b)
4(c)13(d)22(c)31(c)40(c)
5(a)14(a)23(c)32(a)41(a)
6(b)15(a)24(a)33(d)42(b)
7(d)16(c)25(a)34(c)43(a)
8(a)17(d)26(a)35(d)44(a)
9(a)18(a)27(b)36(a)45(b)

Detailed Explanations

Q1. (c) Both follow.

All cats are dogs + All dogs are birds = All cats are birds (I follows). Conversion: Some birds are cats (II follows).

Q2. (b) Only II follows.

No tree is flower + All flowers are fruits: can't conclude about trees and fruits definitely. But All flowers are fruits -> Some fruits are flowers. Since no tree is flower, the flowers-part of fruits is tree-free. Trees could still overlap with non-flower fruits. "Some fruits are not trees" -- since flowers are fruits and not trees, there exist fruits (flowers) that are not trees. II follows. "No tree is fruit" fails because trees might be fruits through a different path.

Q3. (c) Either I or II follows.

Some+Some = no definite conclusion. I (Some pens are books) and II (No pen is book) are complementary (I/E pair).

Q4. (c) Both follow.

All students are scholars + No scholar is lazy = No student is lazy (I). All students are scholars -> Some scholars are students (II).

Q5. (a) Only I follows.

Some apples are oranges + All oranges are mangoes = Some apples are mangoes (I). "All mangoes are oranges" -- reverse of P2, not valid (II fails).

Q6. (b) Only II follows.

All cars are buses + Some buses are trains: All+Some = no definite conclusion about cars and trains. Some buses are trains -> Some trains are buses (conversion, II follows).

Q7. (d) Neither follows.

No+No = No definite conclusion. No man is boy + No boy is girl: Men and girls may or may not overlap.

Q8. (a) Only I follows.

Some B are C + No C is D -> Some B are not D (I follows). All A are B + Some B are C: no definite A-C conclusion (II fails).

Q9. (a) Only I follows.

Some+All = Some kings are princesses (I). "All princesses are queens" is reverse, not valid (II fails).

Q10. (c) Both follow.

All+All chain. I: All roses are beautiful. II: Some beautiful are red (conversion of All red are beautiful).

Q11. (b) Only II follows.

No chair is table + All tables are wood: chairs and wood may overlap (I fails). But tables are wood and not chairs, so some wood is not chair (II follows).

Q12. (a) Only I follows.

Some M are N + All N are O = Some M are O (I). Some O are P is separate; Some+Some for M-P gives no conclusion (II fails).

Q13. (d) Neither follows.

All doctors are engineers + Some engineers are teachers: All+Some = no definite conclusion.

Q14. (a) Only I follows.

No X is Y + Some Y are Z = Some Z are not X (I). "No X is Z" -- X might overlap with Z outside Y (II fails).

Q15. (a) Only I follows.

All+No: No river is ocean (I). "Some oceans are rivers" contradicts this (II fails).

Q16. (c) Either I or II follows.

Some+Some = no definite conclusion. I and II are I/E complementary pair.

Q17. (d) All follow.

All+All+All chain. All cups are bowls (I), All saucers are bowls (II), Some bowls are cups (III -- conversion).

Q18. (a) Only I follows.

Some+All: Some birds are fish (I). "All fish are birds" is not valid (II fails).

Q19. (c) Both follow.

All+No: No politician is corrupt (I). All politicians are honest -> Some honest are politicians (II).

Q20. (d) All follow.

Some+All: Some books are erasers (I). All+No: No pen is sharpener (II). From I + No eraser is sharpener: Some books are not sharpeners (III).

Q21. (a) Only I follows.

All+No: No singer is painter (I). "Some painters are singers" contradicts this (II fails).

Q22. (c) Either I or II follows.

Some+Some = no conclusion. I (All phones are tablets) and II (Some phones are not tablets) are A/O complementary.

Q23. (c) All follow.

All X are Y + No Y is Z = No X is Z (I). Some Z are W -> Some W are Z (III). No Y is Z + Some Z are W: those W that are Z are not Y -> Some W are not Y (II).

Q24. (a) Only I follows.

Some+All: Some girls are natural (I). "All natural are beautiful" is reverse (II fails).

Q25. (a) Only I follows.

No A is B + All B are C: B is in C but not in A. Some C (the B part) are not A (I). "No A is C" fails -- A might overlap non-B part of C.

Q26. (a) Only I follows.

Some tall are rivers + All rivers are deep = Some tall are deep (I). All mountains are tall + Some tall are rivers = no definite mountains-rivers conclusion, so no mountains-deep conclusion (II fails).

Q27. (b) Only II follows.

Some+Some = no red-green conclusion (I fails). Some blue are green -> Some green are blue (II, conversion).

Q28. (a) Only I follows.

All P are Q + All Q are R = All P are R (I). Some R are S gives no P-S conclusion (II fails).

Q29. (b) Only II follows.

No sun is moon + All moons are stars: suns and stars may overlap (I fails). All moons are stars -> Some stars are moons (II).

Q30. (d) All follow.

Some poets are writers + All writers are artists = Some poets are artists (I). All writers are artists + No artist is scientist = No writer is scientist (II). From I + No artist is scientist: Some poets are not scientists (III).

Q31. (c) Both follow.

All+All+No chain. All balls are spheres (II). All spheres + No sphere flat = No ball is flat (I).

Q32. (a) Only I follows.

Some keys are locks + No lock is door = Some keys are not doors (I). "All keys are doors" contradicts this (II fails).

Q33. (d) Neither follows.

All tigers are animals + Some animals are dangerous: All+Some = no conclusion about tigers and dangerous. "All dangerous are animals" reverses P1-context, not valid.

Q34. (c) Both follow.

Some+All: Some sweet are bitter (I). Conversion: Some bitter are sweet (II).

Q35. (d) All follow.

All+All: All diamonds are stones (II). No stone is metal: No diamond is metal (I). All gems are stones -> Some stones are gems (III).

Q36. (a) Only I follows.

No fish is bird + Some birds are black: those birds that are black are not fish -> Some black are not fish (I). "No fish is black" -- fish might be black outside the bird set (II fails).

Q37. (c) Both follow.

All tea is coffee + No coffee is milk = No tea is milk (I). All tea is coffee -> Some coffee is tea (II).

Q38. (a) Only I follows.

Some+All: Some teachers are loved (I). "All loved are kind" reverses P2, not valid (II fails).

Q39. (b) Only II follows.

All+Some: no definite elephant-grey conclusion (I fails). Some big are grey + No grey is white = Some big are not white (II).

Q40. (c) Either I or II follows.

Some A are B + All B are C = Some A are C (definite). But "All A are C" (I) and "Some A are not C" (II) -- I is not definite, II is not definite. They form an A/O complementary pair. Either I or II.

Q41. (a) Only I follows.

All+All: All squares are parallelograms (I). Some parallelograms are rhombuses + All squares are parallelograms: no definite squares-rhombuses link (II fails).

Q42. (b) Only II follows.

No computer is phone + All phones are smart: computers and smart may overlap (I fails). Phones are smart and not computers -> Some smart are not computers (II).

Q43. (a) Only I follows.

Some drugs are chemicals + All chemicals are harmful = Some drugs are harmful (I). All medicines are drugs + Some drugs are harmful: no definite medicine-harmful link (II fails).

Q44. (a) Only I follows.

Some singers are dancers + All dancers are artists = Some singers are artists (I). Some actors are singers + Some singers are dancers: Some+Some = no definite actor-artist link (II fails).

Q45. (b) I and III follow.

All roses are jasmine + No jasmine is lily = No rose is lily (I). All roses are jasmine -> Some jasmine are roses (III). Some lilies are lotus: no definite jasmine-lotus conclusion but "Some lotus are not jasmine" needs testing. Lilies and jasmine are separate (No jasmine is lily), lotus may or may not be jasmine, so we can't definitively say some lotus are not jasmine. II does not necessarily follow.

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