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If A is a set with n(A)=m, then nP(A))=...

If A is a set with `n(A)=m`, then `nP(A))`=

A

(a)`2^(m)`

B

(b)`2^(m-1)`

C

(c)`2^(m)-1`

D

(d)`2^(m+1)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find \( n(P(A)) \) given that \( n(A) = m \). Here’s the step-by-step solution: ### Step 1: Understand the notation - \( n(A) \) denotes the number of elements in set \( A \). - \( P(A) \) denotes the power set of \( A \), which is the set of all subsets of \( A \). ### Step 2: Determine the size of the power set - The number of elements in the power set \( P(A) \) can be calculated using the formula: \[ n(P(A)) = 2^{n(A)} \] - Since we know \( n(A) = m \), we can substitute \( m \) into the formula. ### Step 3: Substitute the value - Substitute \( n(A) \) with \( m \): \[ n(P(A)) = 2^{m} \] ### Final Answer Thus, the number of elements in the power set \( P(A) \) is: \[ n(P(A)) = 2^{m} \]
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