Q.(e) Number of subsets, a set of 4 elements can have, is

The cardinality $n(A)$ of a finite set is its element count. Since simply adding $n(A)+n(B)$ double-counts any overlap, the inclusion-exclusion principle corrects for it: $n(A\cup B) = n(A)+n(B)-n(A\cap B)$ for two sets, extending to $n(A\cup B\cup C) = n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$ for three — the standard tool behind every overlapping-category business survey. Separately, the **Carte …