## 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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