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set theoretic operator
The '''symmetric difference''' between two sets A and B (denoted AΔB) is given as:
<math>A\Delta B = (A\backslash B)\cup (B\backslash A)</math>.
This operator is [[symmetry|symmetric]] in that AΔB=BΔA. Also, AΔA is the empty set, while the symmetric difference of the empty set with any set is that set.
The set-theoretic operator Δ obeys several laws:
<math>
A\Delta (C\backslash B) = (A\Delta C)\backslash B
</math>
<math>
A\Delta \cup_{i\in I} B_i = \cup_{i\in I} A\Delta B_i
</math>
<math>
A\Delta \cap_{i\in I} B_i = \cap_{i\in I} A\Delta B_i
</math>
<math>
A\Delta (B\Delta C) = (A\Delta B)\cap (A\Delta C)
</math>
Symmetric differences are used to create [[filters]] for [[forcing]] constructions.
[[Category:Set_theory]]
<math>A\Delta B = (A\backslash B)\cup (B\backslash A)</math>.
This operator is [[symmetry|symmetric]] in that AΔB=BΔA. Also, AΔA is the empty set, while the symmetric difference of the empty set with any set is that set.
The set-theoretic operator Δ obeys several laws:
<math>
A\Delta (C\backslash B) = (A\Delta C)\backslash B
</math>
<math>
A\Delta \cup_{i\in I} B_i = \cup_{i\in I} A\Delta B_i
</math>
<math>
A\Delta \cap_{i\in I} B_i = \cap_{i\in I} A\Delta B_i
</math>
<math>
A\Delta (B\Delta C) = (A\Delta B)\cap (A\Delta C)
</math>
Symmetric differences are used to create [[filters]] for [[forcing]] constructions.
[[Category:Set_theory]]