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Statement - I: In each of the questions given below, there are two statements A and B. Analyse these two statements and then select the correct answer to the question on the basis of these statements.
Both statements A and B are true and B is the correct explanation of A.
Both statements A and B are true but B is not the correct explanation of A.
Statement A is true but Statement B is false.
Statement A is false but Statement B is true.
Statement A is false but Statement B is true.
In syllogisms where all statements are universal affirmatives (All A are B), any 'Some' conclusion involving the same two items will logically follow as a subset.
In syllogisms where all statements are universal affirmatives (All A are B), any 'Some' conclusion involving the same two items will logically follow as a subset.
Analyze Statements
1. All bats are balls: Bats are a subset of Balls. 2. All balls are wickets: Balls are a subset of Wickets. (Combined: Bats тКВ Balls тКВ Wickets). 3. No wickets are gloves: Wickets are disjoint from Gloves.
Evaluate Conclusion (I): Some balls are bats
Since 'All bats are balls' is given, the converse 'Some balls are bats' is logically true because the set of bats is contained within the set of balls.
Evaluate Conclusion (II): Some wickets are balls
Since 'All balls are wickets' is given, it implies that the space occupied by balls is also occupied by wickets. Therefore, 'Some wickets are balls' must be true.
A: Incorrect because both conclusions are valid. B: Incorrect because both conclusions are valid. C: Incorrect because both conclusions are valid.
D is correct because both conclusions directly follow from the containment relationships established in the statements.
In syllogisms, remember that 'All A are B' always validates 'Some A are B' and 'Some B are A'.
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