Section 1.5: Nested Quanties
1. Notation and Examples of Nested Quantiers
Let P (x, y) be a proposition function in x, y such
that for any given values of x, y, P (x, y) produces a
proposition. The multiple quantications such
as
xyP (x, y),
xyP (x, y),
xy
Section 1.4: Predicates and Quantiers
1. A Predicate or Propositional Function
P is a statement P (x) involving the variable x such
that P (x) is a proposition for each chosen value of x
from a set D. We call D the domain or universe
of the discourse of P
Section 1.1: Propositional Logic
1. A Proposition is a declarative sentence (that
is, a sentence which declares a fact) that is either
true or false, but NOT both.
Propositions are sometimes denoted by letters such
as p, q, r, s, which are called proposit
Section 1.3: Propositional Equivalences
1. Tautology, Contradiction and Contingency: A compound proposition that is always
true, no matter what the truth values of the propositional variables that occur in it, is called Tautology. A compound proposition t
Section 1.2: Applications of Propositional
Logic
1. Translating English Sentences: we can
translate English sentences into expressions involving propositional variables such as p, q, r (which represent propositions) and logical operators or connectives (s