Question

(A Å B) Å(C Å D) = (A Å D) Å (B Å C)

where Å is the Symmetric Difference

Answer 1

Answer on Question #48773 – Math – Discrete Mathematics

$$(A \triangle B) \triangle (C \triangle D) = (A \triangle D) \triangle (B \triangle C).$$

Solution.

Prove this statement by using commutativity and associativity of a symmetric difference:

$$\begin{array}{l} (A \triangle B) \triangle (C \triangle D) = ((A \triangle B) \triangle C) \triangle D = ((B \triangle A) \triangle C) \triangle D = \\ = (B \triangle (A \triangle C)) \triangle D = (B \triangle (C \triangle A)) \triangle D = B \triangle ((C \triangle A) \triangle D) = \\ = B \triangle (C \triangle (A \triangle D)) = (B \triangle C) \triangle (A \triangle D) = (A \triangle D) \triangle (B \triangle C). \end{array}$$

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