GATE CSE 2021 Set 1 | GA Question: 9

Question

Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$

• $\text{Statement 1:}$ All bacteria are microorganisms.
• $\text{Statement 2:}$ All pathogens are microorganisms.

• $\text{Conclusion I:}$ Some pathogens are bacteria.
• $\text{Conclusion II:}$ All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically $\text{CORRECT}$?

• A. Only conclusion $\text{I}$ is correct
• B. Only conclusion $\text{II}$ is correct
• C. Either conclusion $\text{I}$ or $\text{II}$ is correct
• D. Neither conclusion $\text{I}$ nor $\text{II}$ is correct

Comments

Someone  plzz challenge this question...

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I think answer should be D: neither 1 nor 2
EXPLAINATION
Either-OR is similar to XOR gate which means both conclusions can't be true at the same time.
But in the question both conclusions can be true at same time.
So, option D): neither 1 nor 2 is correct seems most logical answer.

NOTE
conclusion 2 means :- Not every Pathogen is Bacteria. which means some pathogens can be bacteria.

Hope You Understand.

But i think marks should be awarded to all as the conclusion 2 could have different meanings.
but still option D is necessarily true.

 

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Congratulations Guys. Both answers are correct as per final answer key..

WE WON!!!

Answer 1

A lot of ambiguity around the question. Here’s my take:

 

EITHER, what does it mean?

Found some articles comparing it to XOR

Either A or B

This means either A can be true OR B can be true, both can’t be true together and can’t be false together

 

https://math.stackexchange.com/questions/68333/what-is-the-logical-connective-for-either-or

https://english.stackexchange.com/questions/95559/can-either-mean-both-any-and-both

https://thewritepractice.com/how-to-use-either-neither-or-and-nor-correctly/

 

For this context, either conclusion 1 has to be true OR conclusion 2 has to be true

 

But for cases where either bacteria is a subset of pathogens or pathogens is a subset of bacteria or both are equal (while all being microorganisms), these are three valid possible conclusions, which are outside of the consideration of the provided conclusions

 

So we have options other than conclusion 1 or 2, because of which, we CAN’T say either one of them is true, both of them can be false, which can’t be allowed as per the meaning of EITHER-OR

 

So, NEITHER 1 nor 2 is NECESSARILY correct

 

Thus, D.

Answer 2

I don't know why answer c is wrong the guy above itself give answer is c though he write d some times first diagram true and sometime below two will be true so we can infer easily that either or will be true , where is the problem,it's quite trivial to see .

The answer will definitely change to c I am sure in this regard

Comments

if all pathogens are bacteria ,does it imply soome pathhogens are bacteria?

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@debmalyaSEN yes, for all--> there exists

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A lot has been said about this question already. I guess I would have been onboard with option C if it had said “Either one is correct but not both”. Now let us see what GATE ans key says.

https://math.stackexchange.com/questions/2130327/does-either-make-an-exclusive-or

It’s hard to say whether “either or” is inclusive or exclusive. According to these answers, inclusive-or is far more common and is the convention. If GATE setters had written as “either I or II is true” (some sort of emphasis) then also it would have unambiguously meant exclusive or.

In contrast, “neither nor” unambiguously translates to (not A and not B) [can use deMorgan’s laws to check].

Answer 3

Let’s end this :D

In the question

• Conclusion I:Conclusion I: Some pathogens are bacteria.
• Conclusion II:Conclusion II: All pathogens are not bacteria

There can be two possible cases

Consider Case 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Where bacteria and pathogen are both subsets of microorganisms &

 Bacteria ∩ Pathogen = null

For this case 

 Conclusion I fails but conclusion II passes 

So we rule out Option A & D

Consider Case 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Where bacteria and pathogen are both subsets of microorganisms &

 Bacteria ∩ Pathogen = not null

For this case 

 Conclusion I passes but conclusion II fails

So we rule out Option B now

Now the question doesn’t say if its OR or XOR

and only conclusive logic we can derive is XOR 

So C satisfies either one of the conditions at a time

It can never satisfy both or none cause its like 

Schrödinger's cat experiment

The cat can either be alive or dead

It cannot be both dead or alive

Nor it cannot be both not dead not alive

So Final ANSWER C :D

Please fell free to try to correct a question which you definitely messed up. :D

 

Comments

It’s answer should be C only there is no way to falsify both conclusion at same time .

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I_am_winner if you find a good solution then please paste here too I want to challenge too

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I will also need if we get proper reasoning brother.Anyway please share anything you get .

Answer 4

Answer is D:

Everyone is debating over C and D,

Option C: Either conclusion I or II is correct.

Remember when pathogens and Bacteria Intersects. Both the conclusions hold..therefore C cannot be the answer...D is correct

Comments

In all the possible cases either 1 occurs or 2 occurs or both occurs .

So neither 1 nor 2 is also false .

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What do you think? What does Either or mean?

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Obviously Either or means only one should happen .

So it is either or is not correct answer .

But also neither nor is not correct

U have seen ECE question of same type ?

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Yes bro I’ve looked at the question asked in ECE, Both questions are completely different.

ECE Question is 
 

• Statement 1Statement 1: All purple are green.
• Statement 2Statement 2: All black are green.

 

• Conclusion IConclusion I: Some black are purple.
• Conclusion IIConclusion II: No black is purple.
  
  
  Answer is C Either conclusion II or IIII is correct.
  
  Now read the conclusion II of CS and ECE. There is huge difference.
  In case of ECE both conclusions cannot hold at the same time. But its happening in case of question asked in Set 1..Just try and draw ven diagram of both questions..you will understand..I dunno how to draw ven diagram here..
  
  When you take the intersection of purple and green..you will notice only conclusion one will be true, conclusion 2 will be false..hence C is the answer but in the case of the question asked in CS when we draw ven diagram you will notice both are true which is not allowed in either or…
  
  Just a small thing i want to say don’t try and apply much of mathematics and dive into this question. If you ask the same question from people who prepare for govt exams they will always say D is the correct answer, I dunno why people are complicating this question like anything when this question can be solved in less than 30 seconds..and straight away most of the answers can be eliminated…