UPSC Prelims 2020·CSAT·Logical Reasoning·Deductive Logic

Two Statements are given followed by two Conclusions: Statements: All numbers are divisible by 2. All numbers are divisible by 3. Conclusion- I All numbers are divisible by 6. Conclusion- II All numbers are divisible by 4. Which of the above Conclusions logically follows/follow from the two given Statements?

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  1. AOnly Conclusion-ICorrect
  2. B(b) Only Conclusion-II
  3. C(c) Neither Conclusion-I nor conclusion-II
  4. D(d) Both Conclusions-I and Conclusion-II

Explanation

Explanation: Conclusion-I: If a number is divisible by both 2 and 3, it must be divisible by their Least Common Multiple (LCM). The LCM of 2 and 3 is 6. Therefore, if all numbers are divisible by 2 and all numbers are divisible by 3, then all numbers must be divisible by 6. Conclusion-I logically follows. Conclusion-II: The statements say all numbers are divisible by 2 and 3. Divisibility by 2 does not automatically imply divisibility by 4. For example, 6 is divisible by 2 but not by 4. The statements do not provide enough information to conclude that all numbers are divisible by 4. Conclusion-II does not logically follow. Since only Conclusion-I follows, option A is correct.
Logical Reasoning: Two Statements are given followed by two Conclusions: Statements: All numbers are divisible by 2. All numbers are divisi

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