Tip #1
Solve the questions through a Venn Diagram. Always make sure common areas are shaded do give you a correct answer.
Tip #2
Shortcut rules (if Venn Diagrams are confusing you) between Statement 1 and Statement 2 in that order
Tip #3
You can cancel out common terms in two statements given, then on the remaining terms apply the syllogisms rules and solve.
E.g. Some dogs are goats, All goats are cows. Cancel out "goats" which leaves us with Some dogs are...all are cows. Important words remaining are ALL and SOME in that order.
SOME + ALL = SOME, hence conclusion is SOME dogs are cows.
Tip #4
Interchange between reading the question as well as the conclusion before arriving at the answers. Always evaluate each and every conclusion to find out how many conclusions are possible.
Tip #5
Avoid using common knowledge as Syllogisms questions usually state unnatural statements
Tip #6
Remember some implications All <=> Some, e.g. All A are B also implies Some A are B (being a subset) and Some B are A Some <=> Some, e.g. Some A are B also implies Some B are A No<=> No, e.g. No A are B also implies No B are A.
In each question below, there are two or three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from
the given statements.
1. Statements: Some boys are girls.
All girls are students.
Conclusions:
I. Some boys are students.
II. Some students are boys.
III. Some students are girls.
IV. All students are girls.
(a) I, II and III follow
(b) II, III and IV follow
(c) I, III and IV follow
(d) I, II and IV follow
(e) All follow
2. Statements: All books are watches.
Some watches are clips.
Conclusions:
I. Some watches are books.
II. No watches are books.
III. Some books are clips.
IV. No books are clips.
(a) I,and III follow
(b) Only I follow
(c) Either I or II follows
(d) Either III or IV and I follow
(e) Either I or II and III follow.
3. Statements:
A. All thieves are men.
B. All men are graduates.
C. No graduates are employed.
Conclusions :
I. Some graduates are thieves.
II. No employed are thieves.
III. Some men are thieves.
IV. Some employed are men.
(a) I, II and III follow
(b) II, III and IV follow
(c) Only I and II follow
(d) Only II and II follow
(e) Only II and IV follow.
4. Statements:
A. Some books are pens
B. All tables are chairs.
C. No pens are tables.
Conclusions:
I. Some books are not tables.
II. Some pens are not chairs.
III. Some books are not chairs.
IV. Some chairs are not pens
(a) I, and IV follow
(b) II, and IV follow
(c) I and III follow
(d) II and III follow
(e) III, and IV follow.
5. Statements: All pigs are elephants.
No pigs are bakers.
Conclusions :
I. Some bakers are not pigs.
II. Some pigs are not bakers.
III. Some elephant are not bakers.
IV. Some bakers are not elephants
(a) I, II and III follow
(b) I, II and IV follow
(c) I, III and IV follow
(d) II, III and IV follow
(e) All follow
6. Statements:
A. All books are notes.
B. Some notes are pencils.
C. No pencils are papers.
Conclusions:
I. Some notes are books.
II. Some pencils are books.
III. Some books are papers.
IV. No books are papers.
(a) Only I follows
(b) Only I and either III or IV follows
(c) Either III or IV follows
(d) Only I and III follow
(e) None of these.
Solutions:
1. a. I + A = I. The conclusion is Some boys are students which is I. This can be converted to Some students are boys, which is II. Some students are girls follows from All girls are students.
2. d. A+ I pair has no definite conclusion. But conclusion I follows directly from All books are watches. III and IV are a complementary pair.
3. a. Conclusion drawn from statements A and B is All thieves are graduates. Conclusion I is obvious from this sentence. III is obvious from statement A. Also A + A + E = A + E = E. Conclusion drawn from all the three is No thieves are employed. II is obvious from this sentence.
4. a. I follows from statements A and C. IV follows from statements C and B. No other conclusion is possible
5. a. The aligned pair is No backers are pigs. All pigs are elephants. E + A = O*. Hence the conclusion is Some elephants are not bakers. Thus III follows. No pigs are bakers implies that No bakers are pigs. I is obvious from this sentence. II follows directly from No pigs are bakers. Hence I, II and III follow.
6. b. Conversion of A gives Some notes are books. Therefore I follows. For II A and B are the relevant statements. But A + I - type pair has no conclusion. So II is not valid. For III all the statements are relevant. No definite conclusion can be obtained from this combination. But conclusions III and IV form a complementary pair.Hence either conclusion III or conclusion IV follows.
Solve the questions through a Venn Diagram. Always make sure common areas are shaded do give you a correct answer.
Tip #2
Shortcut rules (if Venn Diagrams are confusing you) between Statement 1 and Statement 2 in that order
- All + All = All
- All + No = No
- All + Some = No Conclusion
- Some + All = Some
- Some + Some = No Conclusion
- Some + No = Some Not
- No + No = No Conclusion
- No + All = Some not reversed
- No + Some = Some not reversed
Tip #3
You can cancel out common terms in two statements given, then on the remaining terms apply the syllogisms rules and solve.
E.g. Some dogs are goats, All goats are cows. Cancel out "goats" which leaves us with Some dogs are...all are cows. Important words remaining are ALL and SOME in that order.
SOME + ALL = SOME, hence conclusion is SOME dogs are cows.
Tip #4
Interchange between reading the question as well as the conclusion before arriving at the answers. Always evaluate each and every conclusion to find out how many conclusions are possible.
Tip #5
Avoid using common knowledge as Syllogisms questions usually state unnatural statements
Tip #6
Remember some implications All <=> Some, e.g. All A are B also implies Some A are B (being a subset) and Some B are A Some <=> Some, e.g. Some A are B also implies Some B are A No<=> No, e.g. No A are B also implies No B are A.
In each question below, there are two or three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from
the given statements.
1. Statements: Some boys are girls.
All girls are students.
Conclusions:
I. Some boys are students.
II. Some students are boys.
III. Some students are girls.
IV. All students are girls.
(a) I, II and III follow
(b) II, III and IV follow
(c) I, III and IV follow
(d) I, II and IV follow
(e) All follow
2. Statements: All books are watches.
Some watches are clips.
Conclusions:
I. Some watches are books.
II. No watches are books.
III. Some books are clips.
IV. No books are clips.
(a) I,and III follow
(b) Only I follow
(c) Either I or II follows
(d) Either III or IV and I follow
(e) Either I or II and III follow.
3. Statements:
A. All thieves are men.
B. All men are graduates.
C. No graduates are employed.
Conclusions :
I. Some graduates are thieves.
II. No employed are thieves.
III. Some men are thieves.
IV. Some employed are men.
(a) I, II and III follow
(b) II, III and IV follow
(c) Only I and II follow
(d) Only II and II follow
(e) Only II and IV follow.
4. Statements:
A. Some books are pens
B. All tables are chairs.
C. No pens are tables.
Conclusions:
I. Some books are not tables.
II. Some pens are not chairs.
III. Some books are not chairs.
IV. Some chairs are not pens
(a) I, and IV follow
(b) II, and IV follow
(c) I and III follow
(d) II and III follow
(e) III, and IV follow.
5. Statements: All pigs are elephants.
No pigs are bakers.
Conclusions :
I. Some bakers are not pigs.
II. Some pigs are not bakers.
III. Some elephant are not bakers.
IV. Some bakers are not elephants
(a) I, II and III follow
(b) I, II and IV follow
(c) I, III and IV follow
(d) II, III and IV follow
(e) All follow
6. Statements:
A. All books are notes.
B. Some notes are pencils.
C. No pencils are papers.
Conclusions:
I. Some notes are books.
II. Some pencils are books.
III. Some books are papers.
IV. No books are papers.
(a) Only I follows
(b) Only I and either III or IV follows
(c) Either III or IV follows
(d) Only I and III follow
(e) None of these.
Solutions:
1. a. I + A = I. The conclusion is Some boys are students which is I. This can be converted to Some students are boys, which is II. Some students are girls follows from All girls are students.
2. d. A+ I pair has no definite conclusion. But conclusion I follows directly from All books are watches. III and IV are a complementary pair.
3. a. Conclusion drawn from statements A and B is All thieves are graduates. Conclusion I is obvious from this sentence. III is obvious from statement A. Also A + A + E = A + E = E. Conclusion drawn from all the three is No thieves are employed. II is obvious from this sentence.
4. a. I follows from statements A and C. IV follows from statements C and B. No other conclusion is possible
5. a. The aligned pair is No backers are pigs. All pigs are elephants. E + A = O*. Hence the conclusion is Some elephants are not bakers. Thus III follows. No pigs are bakers implies that No bakers are pigs. I is obvious from this sentence. II follows directly from No pigs are bakers. Hence I, II and III follow.
6. b. Conversion of A gives Some notes are books. Therefore I follows. For II A and B are the relevant statements. But A + I - type pair has no conclusion. So II is not valid. For III all the statements are relevant. No definite conclusion can be obtained from this combination. But conclusions III and IV form a complementary pair.Hence either conclusion III or conclusion IV follows.
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