Logical connectives and quantifiers
In order to make compound propositions, we need to define logical connectives. In order to specify quantities of variables, we need to define logical quantifiers. The following is a form of first-order logic (Wikipedia 2019).
Logical connectives
A proposition can be either true \(\top\) and false \(\bot\). When it does not contain a logical connective, it is called an atomistic proposition. To combine propositions into a compound proposition, we require logical connectives. They are not (\(\lnot\)), and (\(\land\)), and or (\(\lor\)). Tbl. ¿tbl:logic-truth-table? is a truth table for a number of connectives.
Quantifiers
Logical quantifiers allow us to indicate the quantity of a variable. The universal quantifier symbol \(\forall\) means “for all”. For instance, let \(A\) be a set; then \(\forall a \in A\) means “for all elements in \(A\)” and gives this quantity variable \(a\). The existential quantifier \(\exists\) means “there exists at least one” or “for some”. For instance, let \(A\) be a set; then \(\exists a \in A \ldots\) means “there exists at least one element \(a\) in \(A\) ….”
Online Resources for Section 2.2
No online resources.