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Q.

 Statement 1: If B=UA then n(B)=n(U)n(A) where U is universal set. 

 Statement 2: For any three arbitrary sets A,B,C we have  if C=AB then n(C)=n(A)n(B) . 

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a

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1. 

b

statement I is true, statement 2 is true; statement 2 is not a correct explanation for statement 1. 

c

Statement 1 is true, statement 2 is false

d

statement 1 is false, statement 2 is true. 

answer is C.

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Detailed Solution

 If U is universal set then B=UA=A, for which n(B)=nA=n(U)n(A)

 But for any three arbitrary sets A,B,C we cannot have always n(C)=n(A)n(B) if C=AB as it is not specified here that 

 weather A is universal set or not. In case A is not universal set  we cannot conclude that n(C)=n(A)n(B) . 

Hence, statement 1 is true but statement 2 is false. 

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