The set S consists of the 10 integers 1 to 10
- Thread starter kevin786
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pka
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Notation: \(\displaystyle \|A\|\) stands for the number of elements is \(\displaystyle A\).
\(\displaystyle \|A\cup B\cup C\|=\|A\|+\|B\|+|C\|-\|A\cap B\|\)\(\displaystyle -\|A\cap C\|-\|B\cap C\|+\|A\cap B\cap C\|\).
Let \(\displaystyle A\) be the collection of subsets containing 1.
Let \(\displaystyle B\) be the collection of subsets containing 3.
Let \(\displaystyle C\) be the collection of subsets containing 7.
I will get you started: \(\displaystyle \|A\cap B\|=2^8.\)
Hello, kevin786!
There are: .\(\displaystyle 2^{10} \,=\,1024\) possible subsets.
The number of subsets that do not contain a 1 or a 3 or a 7
. . is the number of subsets of: \(\displaystyle \{2,4,5,6,8,9,10\}\)
This number is: .\(\displaystyle 2^7 \,=\,128.\)
Therefore, the number of subsets that do contain a 1, 3, or 7 is: .\(\displaystyle 1024 - 128 \:=\:896\)
There are: .\(\displaystyle 2^{10} \,=\,1024\) possible subsets.
The number of subsets that do not contain a 1 or a 3 or a 7
. . is the number of subsets of: \(\displaystyle \{2,4,5,6,8,9,10\}\)
This number is: .\(\displaystyle 2^7 \,=\,128.\)
Therefore, the number of subsets that do contain a 1, 3, or 7 is: .\(\displaystyle 1024 - 128 \:=\:896\)