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\( \rightarrow \) no. of element \( n(A)=m \)If the ratis of cardinal no of powurset of a to cardinal \( h 10 \) of power set of \( B=64: 1 \) \( n(A)+n(B)=12 \). Find the value of \( A \). |
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Answer» Let n(A) = m, n(B) = n. ∴ m + n = 12 (given) \(2^m : 2^n = 64 : 1\) ⇒ \(\frac{2^m}{2^n} = 2^6\) ⇒ \(2^m = 2^{n + 6}\) ⇒ m = n + 6 ⇒ m = (12 -m) + 6 ⇒ 2m = 18 ⇒ m= 9 ∴ n = 3 ∴ n(A) = m = 9. |
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