Statement $$1$$: If $$B=U$$−A 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 $$C=A$$−B then $$n(C)=n(A)$$−$$n(B)$$ .

Question

Statement $$1$$: If $$B=U$$−A 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 $$C=A$$−B then $$n(C)=n(A)$$−$$n(B)$$ .

Infinity Learn · Accepted Answer

If U is universal set then $$B=U$$−$$A=A$$′, 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 $$C=A$$−B 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.

$Statement 1 : If B = U - A then n (B) = n (U) - n (A) where U is universal set.$
$Statement 2 : For any three arbitrary sets A, B, C we have if C = A - B then n (C) = n (A) - n (B) .$

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Statement 1: If B=U−A 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=A−B then n(C)=n(A)−n(B) .

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$Statement 1 : If B = U - A then n (B) = n (U) - n (A) where U is universal set.$
$Statement 2 : For any three arbitrary sets A, B, C we have if C = A - B then n (C) = n (A) - n (B) .$