# 7.12: Introduction to set theory

- Page ID
- 192665

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(1) | ⟦cat⟧ = the set of all cats in the actual world |

(2) | ⟦ Panks ⟧ = the individual Panks in the actual world |

(3) | ⟦ Panks is a cat ⟧ = T if the individual Panks is a member of the set of all cats in the actual world, F otherwise |

(4) | ⟦ Karti is a cat ⟧ = T if the individual Karti is a member of the set of all cats in the actual world, F otherwise |

(5) | A is a subset of B if all members of A are also members of B. |

(6) | A is a proper subset of B if all members of A are also members of B, and there is at least one member of B which is not a member of A. |

###### Table \(\PageIndex{1}\). Set theory notation.

Notation |
Meaning |

A | The set A. Capital letters are used to refer to sets. |

{ a, b, c } |
The set containing members a, b, and c. |

b ∈ A |
b is a member of A. |

d ∉ A |
d is not a member of A. |

A⊆B | A is a subset of B. |

B⊇A | B is a superset of A. |

A⊂B | A is a proper subset of B. |

B⊃A | B is a proper superset of A. |

A = B | A is identical to B (that is, A and B have exactly the same members) |

|A| | The cardinality of A. That is, the number of members in A. |

|A| = 3 | The cardinality of A is equal to 3. That is, there are three members in A. |

A∩B | The intersection of A and B. This set contains objects that are both a member of A and a member of B. |

A∪B | The union of A and B. This set contains objects that are either a member of A or a member of B. |