Mathematics - Algebraic Number Theory
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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)
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The expert examines algebraic number theories in mathematics. A Complete, Neat and Step-by-step Solution is provided in the attached file.
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(i) LHS = A + A = (A - A) (A - A) = { } { } = { } = RHS
(ii) LHS = A + { } = (A - { }) ({ } - A) = ...
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