Test: Syllogism - 1 - Mechanical Engineering MCQ

The least possible Venn diagram is:  

Conclusions:

I. Some white are trucks. → Not follow (As, there is no definite relation between white and trucks. Hence, false)

II. Some horses being truck is a possibility. → Follows (As, some horses are trucks is not definite, but it can be possible)

 Hence, the correct answer is "Only conclusion II follows".

Given Statements:

All birds are crows.

Some crows are parrots.

No crow is a pigeon.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No parrot is a pigeon - False (Because, No definite relation given between parrot and pigeon, so it can be possibly only).

II. Some birds are parrots - False (Because, No definite relation given between birds and parrots, so it can be possibly only).

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 3".

Given Statements:

I. No F is N.

II. All N are L.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All F are L - False (Because, All N are L and no F is N, so those part of N that is L will be definitely not F).

II. All N are F - False (Because, No F is N).

III. Some L are N - True (Because, All N are L so, some L are N is definitely true).

So, Only conclusion III follows.

Hence, the correct answer is "Option 2".

The least possible Venn diagram is:          

Conclusions:

Ⅰ. All tigers are animals. → Follows (As, All tigers are lions and All lions are animals)

Ⅱ. No tigers is a bird. → Do not follow (As, bird is not given in the statement, the relation between bird and tiger cannot be determined)

Hence, only conclusion I follows.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some M are not W → Does not follow (As some X are M, all W are X. So, it is possible but not definitely true)

II. No W is M → Does not follow (As all W are X, some X are M. So,it is possible but not definitely true)

III. Some M are not X → Does not follow (As some X are M. So, it is possible but not definitely true)

∴ Here, None of the conclusions follow.

Hence, the correct answer is "None of the conclusions follow".

Statement:

No plate is a spoon.

Some plates are forks.

All forks are knives.

The least possible diagram for the given statements is as follows:

Conclusions:

(i) Some plates are knives is a possibility - False (Some plates are forks and All forks are knives, so some plates are knives is definitely true).

(ii) No spoon is a fork - False (Because No direct relation given between them, so It can be possible not definite).

Here, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".

The least possible diagram for the given statements is as follows

Conclusion:

I. Some jugs are spoons → False → (As Some jugs are bottles and all spoons are bottles, So some spoon are jugs is possibility but not definite)

II. No spoon is a candy → True → (As all spoons are candy and No bottle is candy, So no spoon is candy is definite true)

III. No jug is a spoon → False → (As some jugs are bottles and all spoons are bottles, So No jug is a spoon is a possibility but not definite)

IV. No jug is a candy → False → (As some jugs are bottles and no bottles are candy, So No jug is candy is it is possible but not definite)

Hence, the correct answer is "Either Conclusion I or III and II follow".

The least possible Venn diagram is:

Conclusions: 

I. Some coaches are nests → TRUE (Some beans are nests and all beans are coaches, so those part of nests that is beams will coaches also).

II. Some beams are jims → FALSE (Because, there is no direct relation given between jims and beans, so it can be possible only).

III. No beam is a jims → FALSE (Because, there is no direct relation given between jims and beans, so it can be possible only).

IV. Some nests are jims → TRUE (Some jims are nests, so some nests are jims also).

Here, Conclusion II and III forms a complementary pair.

So, Both conclusions I and IV and either conclusion II or III follow.

Hence, the correct answer is "Option 3".

Given Statements:

I. All B are V.

II. All K are B.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All K are V - True (Because, All K are B and All B are V gives All K are V).

II. No V is B - False (Because, All B are V).

So, Only conclusion I follows.

Hence, the correct answer is "Option 3".

Statements: I. All Z are Y. II. Some Y are B.

From statement I, "All Z are Y," we understand that Z is a subset of Y. This means every Z is definitely Y.

From statement II, "Some Y are B," we infer that there exists at least one Y that is also B.

Now, let's evaluate each conclusion:

Conclusion I: Some B are not Z.

• This conclusion suggests that there exist some B that do not fall under Z. From the statements, we cannot directly conclude this because we do not have any information about the relationship between B and Z. Therefore, conclusion I does not logically follow from the given statements.

Conclusion II: Some Y are not Z.

• This conclusion states that there are some Y that are not Z. Since statement I tells us that all Z are Y (not necessarily all Y are Z), conclusion II is logically possible. Therefore, conclusion II follows from the given statements.

Conclusion III: Some Z are Y.

• This conclusion is directly stated in statement I ("All Z are Y"). Therefore, conclusion III logically follows from the given statements.

Now, let's match the conclusions with the options:

a) Both conclusions II and III follow.

• Conclusion II (Some Y are not Z) and conclusion III (Some Z are Y) are both logically derived from the statements.

b) Both conclusions I and III follow.

• Conclusion I (Some B are not Z) does not logically follow, but conclusion III (Some Z are Y) does.

c) Only conclusion III follows.

• This option is incorrect because conclusion II also follows.

d) All conclusions follow.

• This option is incorrect because conclusion I does not follow.

Therefore, the correct answer is: a) Both conclusions II and III follow.