Symmetric Difference Distributes over Intersection

Theorem

Symmetric difference is distributive over intersection:

\(\ds R \symdif \paren {S \cap T}\) \(=\) \(\ds \paren {R \symdif S} \cap \paren {R \symdif T}\)


Proof


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Sources

  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebra of sets: $\text {(vi)}$
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