Question

Докажите, что для любых множеств A, B, C:
A∪(B∪C)=(A∪B)∪C

Answer 1

A∪(B∪C)={x | (x∈A)∨(x∈(B∪C))}={x | (x∈A)∨((x∈B)∨(x∈C))}={x | (x∈A)∨(x∈B)∨(x∈C)}={x | ((x∈A)∨(x∈B))∨(x∈C)}={x | (x∈(A∪B))∨(x∈C)}=(A∪B)∪C