Question

discrete

EXERCISE

2.4.2: Symmetric difference applied to many sets.

(a)Calculate A ⊕ B ⊕ C for A = {1, 2, 3, 5}, B = {1, 2, 4, 6}, C = {1, 3, 4, 7}.

Note that the symmetric difference operation is associative: (A ⊕ B) ⊕ C = A ⊕ (B ⊕ C).

(b)Let A, B, and C be any finite sets. Give a concise description for which elements from A, B, and C are in A ⊕ B ⊕ C.

(c)Let A1, A2, …, An be any finite sets. Give a concise description for which elements from A1, A2, …, An are in A1 ⊕ A2 ⊕ … ⊕ An.


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