Examples
Two statements are given below followed by two conclusions numbered as I and II respectively. Consider the given statements as true even if they seem to be not. After reading all the conclusions conform which of the given conclusions logically follows, disregarding commonly known facts.
Q 1 - Statements:
I. Some pigs are bachelors.
II. All bachelors are blessed.
Conclusions:
I. Some pigs are blessed.
II. At least some blessed are bachelors.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : E
Explanation
Some pigs are bachelors (I) + all bachelors are blessed (A) = I + A = I = some pigs are blessed. Hence conclusion I follows. Again all bachelors are blessed - conversion - some blessed are bachelors. Hence conclusion II also follows.
Q 2 - Statements:
I. Some pictures are beds.
II. All beds are trees.
Conclusions:
I. Some pictures are trees.
II. At least some trees are beds.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : E
Explanation
Some pictures are beds (I) + all beds are trees (A) = I + A = I = some pictures are trees. Hence conclusion I follows. Again all beds are trees - conversion - some trees are beds. Hence conclusion II also follows.
Q 3 - Statements:
I. Some ninjas are dogs.
II. No dogs is a liar.
Conclusions:
I. No ninja is a liar.
II. At least some ninjas are liars.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : C
Explanation
Some ninjas are dogs (I) + no dog is a liar (E) = I + E = O = some ninjas are not liars. But conclusion I and II make a complementary pair (I - E). Hence either I or II follows. So option C is correct.
Q 4 - Statements:
I. Some necklace are diagrams.
II. No diagram is a lollipop.
Conclusions:
I. No necklace is a lollipop.
II. At least some necklaces are letters.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : C
Explanation
Some necklaces are diagrams (I) + no diagram is a lollipop (E) = I + E = O = some necklace are not lollipop. But conclusion I and II make a complementary pair (I - E). Hence either I or II follows. So option C.
Q 5 - Statements:
I. Some mangos are brinjals.
II. Some carrots are brinjals.
Conclusions:
I. All mangos are carrots.
II. At least some brinjals are not carrots.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : D
Explanation
Some mangos are brinjals (I) + (some carrots are brinjals (I) - conversion -) some brinjals are carrots (I) = I + I = no conclusion. Hence conclusion I and II do not follow.
Q 6 - Statements:
I. Some rifles are bombs.
II. Some cigars are bombs.
Conclusions:
I. All rifles are cigars.
II. At least some bombs are not cigars.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : D
Explanation
Some rifles are bombs (I) + (some cigars are bombs (I) - conversion -) some bombs are cigars (I) = I + I = no conclusion. Hence conclusion I and II do not follow.
Q 7 - Statements:
I. No cake is a ginger.
II. Some gingers are garlic.
Conclusions:
I. No cake is a garlic.
II. Some garlics are not cakes.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : B
Explanation
No cake is a ginger (E) + some gingers are garlics (I) = E + I = O ∗ = some garlics are not cakes. Hence conclusion II only follows, but I does not follow.
Q 8 - Statements:
I. No cash is a flash.
II. Some flashes are bears.
Conclusions:
I. No cash is a bear.
II. Some bears are not cash.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I nor II follows.
E - If both conclusion I and II follows.
Answer : B
Explanation
No cash is a flash (E) + some flashes are bears (I) = E + I = O ∗ = some bears are not cash. Hence conclusion II only follows, but conclusion I does not follow.
Q 9 - Statements:
I. No pizza is a burger.
II. No chautney is a burger.
Conclusions:
I. Some pizzas are not chautneys.
II. Some burgers are chautneys.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I or II follows.
E - If both conclusion I and II follows.
Answer : D
Explanation
No pizza is a burger (E) + (no chautney is burger-conversion -) no burger is a chautney (E) = E + E = no conclusion. Hence conclusion I does not follow. Again, no chautney is a burger - conversion - no burger is a chautney. Hence conclusion II also does not follow.
Q 10 - Statements:
I. All fingers are levers.
II. Some levers are fringe.
Conclusions:
I. Some fringe are levers.
II. No fingers is a fringe.
A - If only conclusion I follows.
B - If only conclusion II follows.
C - If either conclusion I or II follows.
D - If neither conclusion I or II follows.
E - If both conclusion I and II follows.
Answer : A
Explanation
All fingers are levers (A) + some levers are fringe (I) = A + I = no conclusion. Hence conclusion II does not follow. Again, some levers are fringe (I) - conversion - some fringe are levers (I). Hence conclusion I follows.
Type 1 questions of syllogisms
Instructions: Observe the following statements and select if the conclusion is
Correct/ Incorrect
Example 1:
Major premise: All Actors are right-handed.
Minor premise: All right-handed are Artists.
The conclusion is: Some Artists are Actors.
A. Correct
B. Incorrect
Solution:
Explanation:
Case 1:
The Venn diagram of actors is inside right-handed and which in turn is inside the Venn of artists. According to the diagram, the portion of the red Venn diagram overlapping with green indicates that some actors artist are actors. Hence the conclusion is correct according to this diagram, but can not be concluded as the final answer until the second case is checked.
Case 2: Since all the Venn diagrams are overlapping with each other, according to the diagram all the artists are actors or all the actors are artists. Hence the conclusion is “ some artists are actors” is wrong. Since the conclusion is wrong according to the second Venn diagram. The correct answer will be option B incorrect.
Instructions: Observe the following premises and select if the conclusion is
Correct/ Incorrect
Example 2:
Major premise: No pencil is cloth.
Minor premise: No sweaters are pencils.
The conclusion is: All sweaters are cloth
A. Correct
B. Incorrect
Solution:
Explanation:
In this case, as it can be seen there are three possible scenarios.
Since “ No pencil is cloth” The diagram of pencil and cloth do not have any overlapping and hence they are just touching each other( the diagram can also be represented by keeping them apart, but that will not affect the logical conclusion). According to the minor premise, since no sweaters are pencils the diagrams of sweaters and pencil do not overlap.
Case 1: If no sweaters are pencil, one possibility is there can be no sweater which is no cloth also.
Case 2: There can be a sweater which is also cloth. Hence a part of sweater and cloth overlap with each other.
Case 3: All clothes can be a sweater, as there is not any promise which says this combination is not possible.
The conclusion “all sweaters are cloths” is correct only according to 3rd case but not with respect to the 1st and 2nd case. Hence the conclusion is incorrect.
Type 2 questions of syllogisms.
Observe the following premises and select the correct conclusion.
Example 3:
Major premise: All engineers are innovative.
Minor premise: All students are engineers.
Conclusions:
- All innovative are students
- All students are innovative
- No innovative are students
- No engineers are students
Solution:
Explanation:
The first conclusion “ All innovative are students” is wrong according to case 1 and case 2. The sceond conclusion is correct in all three cases. Conclusion 3 and 4 are not correct according to all the three cases. Hence the correct answer is option B.
Example 4:
Major premise:No computers are televisions.
Minor premise:All radios are televisions.
Conclusions:
- All radios are computers
- No radios are computers
- All computers are radio
- None of the above
Explanation:
The conclusion “ All radios are computers” is not true according to both the Venn diagrams. The second conclusion is true according to both the diagrams as both the Venn diagrams do not overlap with each other anywhere. The conclusion “ All computers are radio” is also wrong according to both the diagrams. Hence the correct answer is option B.
Type 3 questions of syllogisms.
Example 5:
Statements:
- All Stones are Hammers
- No Hammer is Ring
- Some rings are doors
- All doors are windows
Conclusions:
- Some hammers are stones
- Some windows are rings
- Only (1) conclusion follows
- Only (2) conclusion follows
- Either(1) or (2) follows
- Neither(1) nor (2) follows
- Both (1) and (2) follow
Solution:
Explanation:
The first conclusion “Some hammers are stones” is not true according to case 5, where all the shammers are stones. The second conclusion” Some windows are rings “ is true in all the three cases. Hence the correct answer option is B.
Example 6:
Statements:
All cups are books.
All books are shirts.
Conclusions:
i. Some cups are not shirts.
ii. Some shirts are cups.
- Only (1) conclusion follows
- Only (2) conclusion follows
- Either(1) or (2) follows
- Neither(1) nor (2) follows
- Both (1) and (2) follow
Solution:
Explanation:
Four combinations of Venn diagrams are possible according to the two premises. The first conclusion “some cups are not shirts” is not true in all the three cases, as all the cups are shirts in every case. The second conclusion “ some shorts are cups” is true only in the first three cases, whereas in the last case it’s not true(all the shirts are cups). Hence neither conclusion 1 nor 2 is correct. Hence the correct answer is option D.
Candidates can prepare themselves by solving question-related to syllogism and other logical reasoning topics by solving multiple mock tests and previous year question papers:
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