If c is a set with c elements how many elements are in the power set of c

1 answer:

3 0

There would be 2 raised to c elements in the power set. Elements of the power set are formed by making a binary decision on each element of the input set: include or do not include. Since there are two choices for each element of the input set, and there are c elements in the input set, there are 2^c possible arrangements of these input elements.

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Prove:

Using mathemetical induction:

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for n=1

P(n) = $1^{3}+2(1)+3(1)^{2}$ = 6

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Now, for n=k, $n > 0$

P(k) = $k^{3}+2k+3k^{2}$

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = $(k+1)^{3}+2(k+1)+3(k+1)^{2}$

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Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = $n^{3}+2n+3n^{2}$ is divisible by 2 and 3 for all positive integer n.

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Luda [366]

Answer:

Step-by-step explanation:

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You have a good day and good luck on that question

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