(1)
and
Ei ∩ Ej = φ, i ≠ j, i, j = 1, 2, , n
Now, we know that for any event A,
A = A ∩ S
= A ∩ (E1 ∪ E2 ∪ ∪ En)
= (A ∩ E1) ∪ (A ∩ E2) ∪ ∪ (A ∩ En)
Also A ∩ Ei and A ∩ Ej are respectively the subsets of Ei and Ej