Answer:
[tex]2^{11}-1[/tex]
Step-by-step explanation:
The set S = {1, ,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. The total number of elements in the set (n) is 12. The sum of the elements in the set S is even if the sum of the elements of the complement of the set S is odd.
The number of pairs that can give an even sum is therefore [tex]2^{n-1}=2^{12-1}=2^{11}[/tex]
Since the empty set is excluded, The number of pairs that can give an even sum is therefore [tex]= 2^{11}-1[/tex]
