Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.  

Statements:

All spades are diamonds.

All diamonds are hearts.

Conclusions:

(I) Some hearts are spades.

(II) Some spades are hearts.

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OSSC Excise SI (Mains) Official Paper (Held On: 17 Oct, 2024 Shift 1)
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  1. Only conclusion (II) follows.
  2. Only conclusion (I) follows.
  3. Neither conclusion (I) nor (II) follows.
  4. Both conclusions (I) and (II) follow.

Answer (Detailed Solution Below)

Option 4 : Both conclusions (I) and (II) follow.

Detailed Solution

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

qImage67f65f1730ed346e04c1a79bTask Id 1256 Daman (1)

Conclusions:

(I) Some hearts are spades → Follow (As all spades are diamonds and all diamonds are hearts. As whole spades comes in diamonds which whole comes in hearts, therefore it is true.)

(II) Some spades are hearts → Follow (As all spades are diamonds and all diamonds are heartsAs whole spades comes in diamonds which whole comes in hearts, therefore it is true.)

∴ Here, Both conclusions (I) and (II) follow.

Hence, the correct answer is "Option 4".

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