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GATE | GATE CS 2021 | Set 1 | Question 9

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  • Last Updated : 24 May, 2021
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Given below are two statements 1 and 2, and two conclusions I and II

  • Statement 1: All bacteria are microorganisms.
  • Statement 2: All pathogens are microorganisms.
  • Conclusion I: Some pathogens are bacteria.
  • Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct
(B) Only conclusion II is correct
(C) Either conclusion I or II is correct
(D) Neither conclusion I nor II is correct


Answer: (C)

Explanation: We have to find counter example for both given Conclusion, if possible.

  • Case-1 is counter example of Conclusion II, because of all pathogens are bacteria in this diagram.
    Conclusion I would be true in this case, because all so also some.
    (So, Conclusion I is true and II is false.).

  • Case-2 is counter example of Conclusion I, because no pathogens are bacteria.
    Conclusion II would be true in this case, because all so also some.
    (So, Conclusion II is false and II is true.).

  • Case-3: Conclusion I is true, and Conclusion II is false as some pathogens are *already* bacteria.
  • Case-4: Conclusion I is true, and Conclusion II is false as some pathogens are *already* bacteria.

So, we found counter example for both Conclusion. Hence, option (D) is true (Official Key given by GATE 2021.).

Important :
Note that if we consider any image at any point of time or any same domain, then “Either conclusion I or II is correct” as you can also noticed in any given Venn diagram.

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