title: Classical Logic and Its Rabbit-Holes: A First Course
author:  Nelson P. Lande 
description: Many students ask,'What is the point of learning formal logic?' This book gives them the answer. Using the methods of deductive logic, Nelson Lande introduces each new element in exquisite detail, as he takes students through example after example, proof after proof, explaining the thinking behind each concept. Shaded areas and appendices throughout the book provide explanations and justifications that go beyond the main text, challenging those students who wish to delve deeper, and giving instructors the option of confining their course to the basics, or expanding it, when they wish, to more rigorous levels. Lande encourages students to think for themselves, while at the same time providing them with the level of explanation they need to succeed. It is a rigorous approach presented in a style that is informal, engaging, and accessible. Students will come away with a solid understanding of formal logic and why it is not only important, but also interesting and sometimes even fun. It is a text that brings the human element back into the teaching of logic. --Hans Halvorson, Princeton University
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  List of Symbols
  Subject
  Symbol
  Meaning
  Page
  Logic
  ∼p
  not p
  25
  p ∧ q
  p and q
  25
  p ∨ q
  p or q
  25
  p ⊕ q or p XOR q
  p or q but not both p and q
  28
  P ≡ Q
  P is logically equivalent to Q
  30
  p → q
  if p then q
  40
  p ↔ q
  p if and only if q
  45
  ∴
  therefore
  51
  P(x)
  predicate in x
  97
  P(x) ⇒ Q(x)
  every element in the truth set for P(x) is in
  104
  the truth set for Q(x)
  P(x) ⇔ Q(x)
  P(x) and Q(x) have identical truth sets
  104
  ∀
  for all
  101
  ∃
  there exists
  103
  Applications
  of Logic
  NOT
  NOT-gate
  67
  AND
  AND-gate
  67
  OR
  OR-gate
  67
  NAND
  NAND-gate
  75
  NOR
  NOR-gate
  75
  |
  Sheffer stroke
  74
  ↓
  Peirce arrow
  74
  n2
  number written in binary notation
  78
  n10
  number written in decimal notation
  78
  n16
  number written in hexadecimal notation
  91
  Number
  Theory and
  Applications
  d | n
  d divides n
  170
  d |/ n
  d does not divide n
  172
  n div d
  the integer quotient of n divided by d
  181
  n mod d
  the integer remainder of n divided by d
  181
  ⌊x⌋
  the ﬂoor of x
  191
  ⌈x⌉
  the ceiling of x
  191
  |x|
  the absolu