Before talking about sets we need a language for saying true or false. Propositions are the building blocks of every proof: knowing how to combine them with connectives and how to read their truth table is the prerequisite for all of algebra (the operations between sets mirror logic), for all of geometry (“if… then…”) and for the whole study of functions (” continuous and differentiable…”).
Definition — Proposition
A proposition is an assertion for which one can say, without ambiguity, whether it is true (T, or ) or false (F, or ).
“Rome is in Italy” is a proposition (true); “The number is beautiful” is not, because its truth value cannot be established with certainty.
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Topics: Set theory
Concepts: Proposition