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An example of a (7,3,1) difference set in the group / is the subset {,,}. The translates of this difference set form the Fano plane. Since every difference set gives a symmetric design, the parameter set must satisfy the Bruck–Ryser–Chowla theorem. [4]
Universe set and complement notation The notation L ∁ = def X ∖ L . {\displaystyle L^{\complement }~{\stackrel {\scriptscriptstyle {\text{def}}}{=}}~X\setminus L.} may be used if L {\displaystyle L} is a subset of some set X {\displaystyle X} that is understood (say from context, or because it is clearly stated what the superset X ...
The symmetric difference is equivalent to the union of both relative complements, that is: [1] = (), The symmetric difference can also be expressed using the XOR operation ⊕ on the predicates describing the two sets in set-builder notation:
1. The difference of two sets: x~y is the set of elements of x not in y. 2. An equivalence relation \ The difference of two sets: x\y is the set of elements of x not in y. − The difference of two sets: x−y is the set of elements of x not in y. ≈ Has the same cardinality as × A product of sets / A quotient of a set by an equivalence ...
The set of all -subsets of is denoted by (), in analogue with the notation for binomial coefficients, which count the number of -subsets of an -element set. In set theory , the notation [ A ] k {\displaystyle [A]^{k}} is also common, especially when k {\displaystyle k} is a transfinite cardinal number .
If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
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