## Quick Reference

For sets *A* and *B* (subsets of some universal set), the symmetric difference, denoted by *A*+*B*, is the set (*A* ∖ *B*) ∪ (*B* ∖ *A*). The notation *A* Δ *B* is also used. The set is represented by the shaded regions of the Venn diagram shown below. The following properties hold, for all *A*, *B* and *C* (subsets of some universal set *E*):*A*+*A*=Ø, *A*+Ø=*A*, *A*+*A*′=*E*, *A*+*E*=*A*′.*A*+*B*=(*A* ∪ *B*)∖(*A* ∩ *B*)=(*A* ∪ *B*) ∩ (*A*′ ∪ *B*′).*A*+*B*=*B*+*A*, the commutative law.*A*+*B*)+*C*=*A*+(*B*+*C*), the associative law.*A* ∩ (*B*+*C*)=(*A* ∩ *B*)+(A ∩ *C*), the operation ∩ is distributive over the operation+.

*A*+*A*=Ø, *A*+Ø=*A*, *A*+*A*′=*E*, *A*+*E*=*A*′.

*A*+*B*=(*A* ∪ *B*)∖(*A* ∩ *B*)=(*A* ∪ *B*) ∩ (*A*′ ∪ *B*′).

*A*+*B*=*B*+*A*, the commutative law.

*A*+*B*)+*C*=*A*+(*B*+*C*), the associative law.

*A* ∩ (*B*+*C*)=(*A* ∩ *B*)+(A ∩ *C*), the operation ∩ is distributive over the operation+.

*Subjects:*
Mathematics.

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