Question: Prove that A – (B U C) = (A – B) ∩ (A – C)

Answer: Let’s analyze step by step

A−(B∩C)

A∩(B∪C)^{c}

A∩B^{c}∩C^{c}

A∩A∩B^{c}∩C^{c}

A∩B^{c}∩A∩C^{c}

(A∩B^{c})∩(A∩C^{c})

(A−B)∩(A−C)

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# Prove that A – (B U C) = (A – B) ∩ (A – C)

Math, Math Problems and Solutions, Tests, Formulas, Algebra.

Question: Prove that A – (B U C) = (A – B) ∩ (A – C)

Answer: Let’s analyze step by step

A−(B∩C)

A∩(B∪C)^{c}

A∩B^{c}∩C^{c}

A∩A∩B^{c}∩C^{c}

A∩B^{c}∩A∩C^{c}

(A∩B^{c})∩(A∩C^{c})

(A−B)∩(A−C)