Sets and Relations Part 1

Elements of the type 3k=3
Elements of the type 3k+1=1,7,9
Elements of the type 3k+2=2,5,11
Subsets containing one element S1=1
Subsets containing two elements
S2=‌3C1×‌3C1=9
Subsets containing three elements
S3=‌3C1×‌3C1+1+1=11
Subsets containing four elements
S4=‌3C3+‌3C3+‌3C2×‌3C2=11
Subsets containing five elements
S5=‌3C2×‌3C2×1=9
Subsets containing six elements S6=1
Subsets containing seven elements S7=1
⇒‌ sum ‌=43