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No, a relation does not have to contain every possible ordered pair. By definition, a relation is a subset of the Cartesian product $A \times B$, meaning it can include only some of the ordered pairs.

Conditions: A and B are sets.; R is a relation between A and B.

No, a relation does not have to contain every possible ordered pair. By definition, a relation is a subset of the Cartesian product $A \times B$, meaning it can include only some of the ordered pairs.

Conditions: A and B are sets.; R is a relation between A and B.

In a relation diagram, an arrow drawn from an element in the first set to an element in the second set means that the corresponding ordered pair belongs to the relation. It visually encodes the membership of a specific pair in the subset of the Cartesian product.

Conditions: The diagram shows two sets, typically represented as ovals or circles.; An arrow connects an element from the first set to an element from the second set.

In a relation diagram, an arrow drawn from an element in the first set to an element in the second set means that the corresponding ordered pair belongs to the relation. It visually encodes the membership of a specific pair in the subset of the Cartesian product.

Conditions: The diagram shows two sets, typically represented as ovals or circles.; An arrow connects an element from the first set to an element from the second set.