A∩(BΔC) = (A∩B)Δ(A∩C)
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Answer:
Prove
A∩(BΔC)=(A∩B)Δ(A∩C)
without using Venn Diagram
My Try:
we have
A∩(BΔC)=A∩((B∪C)−(B∩C))=A∩((B∪C)∩(B∩C)′)
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A∩(BΔC)=(A∩(B∪C))∩(B′∪C′)
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A∩(BΔC)=((A∩B)∪(A∩C))∩(B′∪C′)
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A∩(BΔC)=((A∩B)∩(B′∪C′))∪((A∩C)∩(B′∪C′))
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A∩(BΔC)=(A∩B∩C′)∪(A∩C∩B′)
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A∩(BΔC)=((A∩B)−C)∪((A∩C)−B)
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