Logical Reasoning - Logical Deduction - Discussion

In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Give answer:

  • (A) If only conclusion I follows
  • (B) If only conclusion II follows
  • (C) If either I or II follows
  • (D) If neither I nor II follows and
  • (E) If both I and II follow.


Statements: All bags are cakes. All lamps are cakes.


  1. Some lamps are bags.
  2. No lamp is bag.

[A]. Only conclusion I follows
[B]. Only conclusion II follows
[C]. Either I or II follows
[D]. Neither I nor II follows
[E]. Both I and II follow

Answer: Option C


Since the middle term 'cakes' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.

Suneel said: (Jan 18, 2011)  
Draw the verner diagram for the above statement.

Mrudula said: (Jan 28, 2011)  
How can we tell that they involve only in the extreme terms and form a complementary pair.

Jaya said: (Apr 24, 2011)  
Both the terms are universal affirmative then conclusion also in universal affirmative?

Balaji said: (May 17, 2011)  
Fellas why using technicals words just can body put it in simple way to understand this problem.

Promel said: (May 26, 2011)  
When no conclusion can be drawn then why can't be the answer be option (D) If neither I nor II follows ?

Aishwarya said: (Jun 16, 2011)  
It is possible that lamps and bags from different groups within the group of cakes or it is possible that some bags and lamps are common?

Rahul said: (Jul 7, 2011)  
Answer is D i think..as common term is not distributed in statement..

Sharath said: (Jul 19, 2011)  
Ya. No conclusion follows. Since the middle term is not at all distributed.

Deepika said: (Aug 1, 2011)  
Let us assume that bag=X, cake=Y & lamp=Z, then from d question it is clearly indicated that X=Y & Z=Y, that means some X=Z which is written in conclusion 1.

But it's contrast statement "NO LAMP IS BAG" is written conclusion 2. so i think the option 1 is the right ans. can any one tell

whether i'm right or wrong ?

Chinu said: (Sep 15, 2011)  
Whats exactly a complementary pair?

Please answer me.

Kapil said: (Nov 7, 2011)  
This question has multiple choices if we go by venn diagram approach. So we must go by selecting the middle term approach which give us unique answer with no conclusion can be drawn as mid term is not distributed.

Zafrul Islam said: (Aug 27, 2012)  
Let us assume that bag=X, cake=Y & lamp=Z, then from d question it is clearly indicated that X=Y & Z=Y, that means either some X=Z
or it may be no terms of z match with the x terms.So c is correct option.

Naveed said: (Oct 2, 2012)  
According to the rule book to the Deduction.

Rule: Atleast one middle term in the premise should be distributed to give conclusion. If both are undistributed then no conclkusion.

In the given question both are undistributed hence no conclusion.

Udaya said: (Nov 3, 2012)  
Please any can explain clearly?

Vipin said: (Jan 22, 2013)  
Only the 1st conclusion follows. The two statements are universal affirmative, so in this case the answer should be either universal affirmative or particular affirmative, there can't be a negative statement as conclusion.

Kumar said: (Feb 3, 2013)  
How to find extreme terms in logical reasoning?

Mayank said: (May 1, 2013)  
What is extreme term and how to find it?

Sathish said: (Sep 13, 2013)  
All (Universal affirmative statement) bags (+) are cakes (-).

All (Universal affirmative statement) lamps (+) are cakes (-).

Here the middle term is cakes (both are minus). At least one plus (+) should contain to follow the conclusion). So here both are minus. Answer is no conclusion.

Soumya said: (Sep 26, 2013)  
Since middle term is not distributed no conclusions can be drawn.

Vik said: (Oct 25, 2013)  
So. If the task were to find SP conclusion - then there should be no conclusion since M was undistributed in both premises.

However, if we draw some circles - we will see that either I or II follows. (that is why we cannot make SP conclusion. But can solve this task).

Vikas said: (Oct 27, 2013)  
Please explain extreme terms?

Prashant said: (Nov 6, 2013)  
If the middle term is not distributed then how could we drawn any conclusion i.e. the answer must be no conclusion and as far as the given options is concerned the answer must be neither I nor II rather than the either I or II.

Please reply what is the correct answer I'm quiet confused.

Srinath said: (Dec 15, 2013)  
Guys do these all kinds of logical deductions by drawing vernier diagrams, then you will not get confusion.

Vyzz said: (Jul 20, 2014)  
Why can't all bags be lamps? So is option 'C' correct?

Pranav Vikram said: (Aug 8, 2014)  
All bags are cakes.
All lamps are cakes.

(Venn Diagram Approach).

Draw a rectangle, name it "cakes"
Lamps and bags will come inside this rectangle, right?
Now draw a circle inside the rectangle and name it "bags"

Now for lamps there are two cases,

i.We can draw a circle "lamps" that overlaps with "bags"

ii. We can draw a circle that is disjoint from "bags"

These are the two options. At a time only one can be true right? (Because two circles can never intersect and be disjoint at the same time).

So the answer is Either.

Sanchita said: (Aug 9, 2014)  
What exactly do we have to follow? the venn diagram approach or subject predicate distributed undistributed conclusions ?

Micheal said: (Aug 31, 2014)  
Can anyone tell me the concept behind this types of problem?

Shuvam said: (May 8, 2015)  
The answer should be D as some lamps are bags and all lamps can also be bags. So here lies the confusion. So the conclusion can be challenged and thus it is D none follows.

Ishu said: (May 24, 2015)  
I think as the middle term is not used in any of the premises conclusion cannot be made. Anyone please clarify my doubt?

Achintya said: (Aug 1, 2015)  
Middle term is not distributed once so no conclusion can be derived.

Prakash said: (Sep 3, 2015)  
Positive questions could result in only positive conclusions. Hence the answer is A.

Dayakar said: (Dec 16, 2015)  
Can you please give clarity on extreme terms?

Jeff said: (Jun 14, 2016)  
Cake is the pool, could be composed of bags and lamps only or more.
All bags are part of the pool.
All lamps are also part of the pool.

If some lamp are bags, it makes the second statement invalid and.
If no lamp is a bag, making statement one invalid.

So only one can be the answer, so either.

Dancy Boy Govind said: (Jun 17, 2016)  
Cake is a pool.

But all bags are part of the pool.
All lamps are also part of the pool.

So the answer is EITHER.

Doodle said: (Jun 30, 2016)  
As per my logic the answer should be D.

Anantha said: (Jul 3, 2016)  
If we use Venn diagram method inside cakes there are lamps and inside lamps there are bags.

So, according to it only statement 1 follows.

Hashi said: (Aug 9, 2016)  
How can we say that no lamp is bag?

Ardhe said: (Aug 9, 2016)  
Statements: All bags are cakes. All lamps are cakes.

Means Some lamps may be bags or may not be bags.

If "may be bag" then conclusion "II. No lamp is bag" will not be valid. Conclusion 1 will only valid.

If "may not be bags" then conclusion "I. Some lamps are bags" will not valid. Only conclusion 2 will valid.

So the answer is C] Either I or II follows.

Abhi said: (Oct 18, 2016)  
According to me, It is inconclusive because all lamps are bags.

Akanksha said: (Nov 30, 2016)  
Can anyone tell me why option B is not correct?

Siddhant said: (Dec 23, 2016)  
Why we are not taking a possibility when the lamp circle is surrounded by bag circle and bag circle by cake circle since also fulfils the condition all lamps are cakes and all bags are cakes?

Hence the answer to the solution should be C.

Chitransh Sinha said: (Jul 7, 2017)  
The answer is C as there are only two possibilities i.e. some lamps are bags or no lamp is a bag. Only one of them has to be correct. One can deduce this using Venn diagram. Option D could have been the correct answer given that the conclusions had one different statement than stated above.

Williams said: (Jul 26, 2017)  
The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form:

P U Q.
Q U R.
Therefore, P U R.
Therefore the answer to the above question is D.

Pratik said: (Apr 1, 2018)  

Think of this question as a Venn-diagram -A big circle for cakes. Inside cakes, there are two circles - one for bags and one for lamps.

Now there are only two possibilities for how the circles inside are drawn, either the two smaller circles intersect(touch at 1 point or intersect at 2 points) or they don't touch at all.

If they intersect, some lamps are bags (and vice versa). If they don't touch, no lamp is bag (and vice versa). These are the only two possibilities, one of these must occur. Hence, they are complementary.

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