If A = 1, 2, 3, 4, , 10 , then the number of non-empty subsets of A containing only even number is

Step-by-step solution

Given set A = 1, 2, 3, 4, , 10 . The subsets must contain only even numbers. The even numbers in set A are 2, 4, 6, 8, 10 . Let E be the set of even numbers in A , so E = 2, 4, 6, 8, 10 . The number of elements in E is n(E) = 5 . The total number of subsets of E is 2^5 = 32 . Since we need the number of non-empty subsets, we subtract the empty set. The number of non-empty subsets of E is 2^5 - 1 = 32 - 1 = 31 . Answer: 31