Set Names and Relationship Cubes in ON-SETS®

(found on the blue symbol cubes)

OPERATION MEANING EXAMPLE (for Universe below)
Universe (Universe) This Set-Name stands for the universe, the set of cards turned face up on the table. Subtraction R = 5 (cards 4, 7-10)
Empty Set (Empty or Null) This Set-Name stands for the empty set, which has no elements. This is not represented by the blank card. Empty Set Complement = 10 (cards 1-10)
(Subset) The subset cube represents the relation of set-inclusion. It is used in making Restriction Statements. When placed between the names of two sets, the result is not a set but a statement about the sets that says that the set named on the left is included in the set named on the right; the first set is a subset of the second set if and only if every element in the first set is also in the second set. It cannot be used in building set names nor can it be played to Forbidden. Using the Restriction Statement B Subset R removes 1 card (4) from the Universe.
Equal (Equal) The equal cube represents the relation of set-identity between the sets. It is used in making Restriction Statements. When placed between the names of two sets, the result is not a set but a statement about the sets that says that the two set names on either side of the equal sign are names for the same set of cards; they are identical if and only if each set contains the same elements. If an element is in one set, then it is in both. It cannot be used in building set names nor can it be played to Forbidden. Its use in expressing a relation between sets is similar to its use in expressing a relation between numbers as in equations. Using the Restriction Statement B Equal R removes 3 cards (4-6) from the Universe.

Sample Universe

Blue Spot
Red Spot
Green Spot
Yellow Spot
Blue Spot
Red Spot
Green Spot
Blank Spot
Blue Spot
Red Spot
Blank Spot
Blank Spot
Blue Spot
Blank Spot
Green Spot
Yellow Spot
Blank Spot
Red Spot
Green Spot
Blank Spot
Blank Spot
Red Spot
Blank Spot
Yellow Spot
Blank Spot
Blank Spot
Green Spot
Yellow Spot
Blank Spot
Blank Spot
Green Spot
Blank Spot
Blank Spot
Blank Spot
Blank Spot
Yellow Spot
Blank Spot
Blank Spot
Blank Spot
Blank Spot
1 2 3 4 5 6 7 8 9 10

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