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Dane są zbiory A={4,6,8,9) i B={1,4,9}. Sprawdź czy zachodzi równość:
(A U B)/(A n B)=(A/B)U(B/A)

Odpowiedź :

Romaviz

A = {4, 6, 8, 9} i B = {1, 4, 9}

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A ∪ B = {4, 6, 8, 9} ∪ {1, 4, 9} = {1, 4, 6, 8, 9}

A ∩ B = {4, 6, 8, 9} ∩ {1, 4, 9} = {4, 9}

(A ∪ B) \ (A ∩ B) = {1, 4, 6, 8, 9} \ {4, 9} = {1, 6, 8}

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A \ B = {4, 6, 8, 9} \ {1, 4, 9} = {6, 8}

B \ A =  {1, 4, 9}  \ {4, 6, 8, 9} = {1}

(A \ B) ∪ (B \ A) = {6, 8} ∪ {1} = {1, 6, 8}

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(A ∪ B) \ (A ∩ B) = {1, 6, 8}

(A \ B) ∪ (B \ A) = {1, 6, 8}

Zatem: (A ∪ B) \ (A ∩ B) = (A \ B) ∪ (B \ A)

Odp. Podana w treści zadania równość zachodzi.

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