determine subsets of odd and even

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foukr

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For any finite set M of size n, determine how many m
subsets of odd and even sizes.

Do you know how to write correct explanation ?

thx
 
How many subsets of M are there? How many of them have sets with an even number of elements?

As already pointed out you need to show work so we know exactly where you are stuck.
 
foukr said:
For any finite set M of size n, determine how many m
subsets of odd and even sizes.

Do you know how to write correct explanation ?
Click to expand...
If this is not the exact wording of the problem as given to you, please quote that -- even if you have translated from another language. I find it almost incomprehensible.

My first though was that an "m subset" would be a subset of size m (I have seen that term used), but that seems redundant, since m is not specified and the size can be even or odd. Maybe you meant "M subsets", meaning "subsets of M"? If so, changing case is a very bad idea.

Then there is the uncertainty whether you are asking two questions (how many subsets of any even size are there, and how many subsets of any odd size are there), or something else.

It may help if you give some examples of what you are asking for, with specific numbers. For example, "For any finite set M of size 5", what would be the answer to your question?
 
foukr said:
For any finite set M of size n, determine how many m subsets of odd and even sizes.
Click to expand...
Hint: when is \(\displaystyle \dbinom{M}{n}=\dfrac{M!}{n!(M-n)!}\) even? Odd?
Recall that \(\displaystyle {2^M} = \sum\limits_{n = 0}^M \dbinom{M}{n} \)
 
Dr.Peterson said:
If this is not the exact wording of the problem as given to you, please quote that -- even if you have translated from another language. I find it almost incomprehensible.

My first though was that an "m subset" would be a subset of size m (I have seen that term used), but that seems redundant, since m is not specified and the size can be even or odd. Maybe you meant "M subsets", meaning "subsets of M"? If so, changing case is a very bad idea.

Then there is the uncertainty whether you are asking two questions (how many subsets of any even size are there, and how many subsets of any odd size are there), or something else.

It may help if you give some examples of what you are asking for, with specific numbers. For example, "For any finite set M of size 5", what would be the answer to your question?
Click to expand...
I thought that m subsets was a typo for subsets. I also thought there was two problems.
 
Have you tried looking at simple sets and counting the even and odd subsets?
For example the set {a} has two subsets, {a} and {}. {a} has an odd number (1) of elements and {} has an even number (0). {a, b} has 4 subsets, {}, {a}, {b}, {a, b}. {a, b, c} has 8 subsets, {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}.

Count how many of those have an even number of elements and how many have an even number of elements? It should become clear!
 
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