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Let A and B be the sets. The symmetric difference between A and B is :

  • A.\(A \oplus B = (A - B) \cup (B - A)\)
  • B.\(A \cup B = (A \oplus B) \cap (B + A)\)
  • C.\(A \cap B = (B + A) - (B - A)\)
  • D.\(A \subseteq B = (A - B) \cup (B + A)\)

Answer: A

The symmetric difference is \(A \oplus B = (A - B) \cup (B - A)\).

It contains the elements that belong to exactly one of the two sets: those in A but not B, together with those in B but not A. Equivalently it is \((A \cup B) - (A \cap B)\).

The other options define union, intersection and subset by formulas that do not hold; for example \((A - B) \cup (B + A)\) is just \(A \cup B\), which is not what \(A \subseteq B\) means, and a subset relation is not a set at all.

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