I am not sure what the set/sets are supposed to be...
1 answer:
Answer:
see the attachment
Step-by-step explanation:
(a) S1 is the set of all subsets of {t, u, v}. There are 2^3 = 8 subsets, the EMPTY set being one of them. They are listed in the attachment.
It seems likely your answer will need to match that shown in the attachment:
{EMPTY, {t}, {u}, ... , {t, u, v}}
where the elements of multi-element sets are listed separately: {t, u}, not {tu}.
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(b) S2 is the set S1 with <em>w</em> added to each subset. (see the attachment for a listing)
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(c) Correct, the sets are disjoint, since every set in S1 is different from every set in S2.
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(d) Each set has 8 elements; the sets are the same size. You know this because you created set S2 from set S1. (See (b), above.)
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(e) The sets are disjoint (see (c)), so the total number of elements in their union is the total of the numbers of elements in each set: 8 + 8 = 16.
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(f) P(A) is undefined here, so none of these questions can be answered.
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The given sequence is
a₁, a₂, ...,
Because the given sequence is an arithmetic progression (AP), the equation satisfied is
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d = the common difference.
The common difference may be determined as
d = a₂ - a₁
The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..
The sum of the first n terms is
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For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100
a₁, a₂, ...,
Because the given sequence is an arithmetic progression (AP), the equation satisfied is
where
d = the common difference.
The common difference may be determined as
d = a₂ - a₁
The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..
The sum of the first n terms is
Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100