# Section 1.1: Problem 1 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

Give three sentences in English together with translations into our formal language. The sentences should be chosen so as to have an interesting structure, and the translations should each contain 15 or more symbols.

1. The citation at the top.

Working problems is a crucial part of learning mathematics | |

Learning mathematics | |

Merely poring over given definitions, theorems, and examples | |

Solving problems | |

The translation of the citation above into readily understandable meaning |

2. Page xi: “Borogoves are mimsy whenever it is brillig. It is now brillig, and this thing is a borogove. Hence this thing is mimsy”.

This is a borogove | |

This is mimsy | |

This is brillig | |

The logic behind the quote above (a tautology) |

3. Equivalence relations.

Relation is reflexive | |

Relation is symmetric | |

Relation is transitive | |

Relation is an equivalence relation | |

If a reflexive and symmetric relation is not an equivalence relation, then it is not transitive |