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Trava [24]
3 years ago
7

Find the mean 9,1,8,3,2,1 graphically.

Mathematics
1 answer:
adelina 88 [10]3 years ago
4 0
10+11+3
21+3
24
24/6
The mean is 4
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Please help with steps:<br><br> 18 - 24 (divide) (-6)
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2 years ago
Verify that |P(A)| = 2^n , if |A| = n for n = 0, 1, 2, 3.
Marizza181 [45]

Answer:

We have to prove that,

|P(A)| = 2^n , if |A| = n for n = 0, 1, 2, 3.

For n = 0,

A = {}

P(A) = { {} } = 2^0 = 1

For n = 1,

A = { a }     ( suppose )

P(A) = { {}, a } = 2^{1} = 2,

For n = 2,

A = { a, b }

P(A) = { {}, {a}, {b}, {a, b} = 2^2 = 4,

For n = 3,

A = { a, b, c },

P(A) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} } = 2^3 = 8

Thus, it is verified for n = 0, 1, 2, 3.

Now, suppose it is valid for a set B having k elements,

That is, |P(B)| = 2^k

Also, there is a set A,

Such that, A = B ∪ {x}

Since, after including the element x in set B,

The element x will be come with every element of set B in the power set of B,

i.e. P(A) = 2^k+2^k = 2^k(1+1) = 2^{k}.2 = 2^{k+1}

Hence, by the induction it has been proved,

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8 0
3 years ago
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