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Chapter 1
A Little Simple Math
1.1 Propositional Logic
Elementary algebra is the mathematics of real numbers and the operators +,
−, ∗ (multiplication), and / (division). Propositional logic is the mathematics
of the two Boolean values true and false and the five operators whose names
(and common pronunciations) are
∧ conjunction (and)
∨ disjunction (or)
¬ negation (not)
⇒ implication (implies)
≡ equivalence (is equivalent to)
To learn how to compute with numbers, you had to memorize addition and
multiplication tables and algorithms for calculating with multidigit numbers.
Propositional logic is much simpler, since there are only two values, true and
false. To learn how to compute with these values, all you need to know are the
following definitions of the five Boolean operators:
∧ F ∧ G equals true iff both F and G equal true. iff stands for if
and only if. Like
most mathematicians, I use or to
mean and/or. ∨ F ∨ G equals true iff F or G equals true (or both do).
¬ ¬F equals true iff F equals false. ⇒ F ⇒ G equals true iff F equals false or G equals true (or both).
≡ F ≡ G equals true iff F and G both equal true or both equal false.
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