« Section 1.1: The Language of Sentential Logic

Section 1.1: Problem 2 Solution »

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