Set Operators

The following operators take sets as operands. Set Operators

Operator

Operation

Operand Types

Result Type

Example

+

union

set

set

Seti + Set2

-

difference

set

set

S - T

*

intersection

set

set

S * T

<=

subset

set

Boolean

Q <= MySet

>=

superset

set

Boolean

Si >= S2

=

equality

set

Boolean

S2 = MySet

<>

inequality

set

Boolean

MySet <> Si

in

membership ordinal, set

Boolean

A in Seti

The following rules apply to +, -, and *.

  • An ordinal o is in X + y if and only if o is in X or y (or both). o is in X - y if and only if o is in X but not in y. o is in X * y if and only if o is in both X and y.
  • The result of a +, -, or * operation is of the type set of a..b, where a is the smallest ordinal value in the result set and B is the largest.

The following rules apply to <=, >=, =, <>, and in.

  • X <= y is True just in case every member of X is a member of y; z >= w is equivalent to w <= z. u = V is True just in case u and V contain exactly the same members; otherwise, u <> V is True.
  • For an ordinal o and a set s, o in s is True just in case o is a member of s.
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