How many subsets of the set \(\{1,2,3,4, 5, 6, 7, 8, 9, 10\}\) contain the number 5?
+2863 There are 2^10 different subsets in the original set.
Now let us just subtract subsets without a 5
Let us just pretend you have set without a 5
So {1 2 3 4 6 7 8 9 10} Is your new set
So how many subsets can you make from that?
2^9 subsets
2^10 - 2^9 = 512 different subsets
NOTE: 2^10 - 2^9 is NOT 2.
So there you have it! :D:D:D
+220 To solve this problem, do this...
There are 10 numbers, so the first term of the expression is 2^10. Then subtract that by 2^9 to find the answer.
2^10 = 1024
2^9 = 512
1024-512 = 512
There are 512 subsets that do not contain the number 5.
~~Hypotenuisance
