How many subsets of set S=\{2,3,4,5,6\} only have even elements?
The answer is 7. In Greg’s video, he mentioned that there’s a trick and immediately jumped into 2^3-1. What’s the trick here? I don’t understand how Greg came up with that expression.
Also, I got the same answer but with a different method, and possibly a misinterpretation of the question? Since they’re asking for subsets, it means that order does not matter. Hence, the only possible subsets of S that contain only even elements are: \{2\} \{4\} \{6\} \{2,4\} \{2,6\} \{4,6\} \{2,4,6\}
And the total is 7. But since the focus of this part of the module is permutations, I think I might have misinterpreted the question.
If I interpret it as permutation question, I would have gotten it wrong. I would think it’s 3!=6.
When number\ of\ elements=0, then number\ of\ subsets =1, because there’s only the empty set.
When number\ of\ elements=1, then number\ of\ subsets =2, because there’s \{a\} and the empty set.
When number\ of\ elements=2, then number\ of\ subsets =4, because there’s \{a\}, \{b\}, \{a,b\}, and the empty set.
When number\ of\ elements=3, then number\ of\ subsets =8, because there’s \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}, and the empty set.
Extrapolating from what I’ve seeing above, number\ of\ subsets =2^n, where n is the number of elements in a set. Interesting, thank you.
Hi, I am opening this thread again because I do think the answer should indeed be 8. Why is the null set not considered in the calculation? It does have 0 elements which is even, and moreover, the question does not explicitly state “even positive” elements.
