Explore BrainMass

Mathematics - Algebraic Number Theory

If A and B are subsets of a set X, define their symmetric difference by
A+B = (A-B) union (B-A)

(i). Prove that A + A= empty set
(ii) Prove that A + empty set= A
(iii) Prove that A + (B+C) = (A+ B) + C
(iv) Prove that A intersection (B+C) = (A intersection B)+(A intersection C)

Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.