Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.  Statements :  Some Rackets are Bats. All Bats are Sticks.  Conclusions :  I. All Rackets are Sticks. II. Some Rackets are not Sticks.  III. Some Sticks are Rackets.?

LohaHridoy
  1. Only conclusion II follows.
  2. Only conclusion III follows.
  3. Both conclusions I and III follow.
  4. Only conclusion I follows.

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AhmedNazir

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Option 2 : Only conclusion III follows.

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

[ alt="F1 Madhuri SSC 29.03.2022 D10" src="//storage.googleapis.com/tb-img/production/22/03/F1_Madhuri_SSC_29.03.2022_D10.png" style="width: 171px; height: 99px;">

Conclusions : 

I. All Rackets are Sticks → False (As Some Rackets are Bats so, All Rackets are Sticks is definitely False as shown below)

[ alt="F1 Madhuri SSC 29.03.2022 D11" src="//storage.googleapis.com/tb-img/production/22/03/F1_Madhuri_SSC_29.03.2022_D11.png" style="height: 123px; width: 123px;">

II. Some Rackets are not Sticks → False (As Some Rackets are Bats and All Bats are Sticks so, Some Rackets are not Sticks is definitely False as shown below)

[ alt="F1 Madhuri SSC 29.03.2022 D12" src="//storage.googleapis.com/tb-img/production/22/03/F1_Madhuri_SSC_29.03.2022_D12.png" style="width: 219px; height: 102px;">

III. Some Sticks are Rackets → True (As Some Rackets are Bats and All Bats are Sticks so, Some Sticks are Rackets is True)

∴ Here Conclusion I and II does not form complimentary pairs because both are false and there is no possibility from given statements.

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

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