# Logic

*By Robert Laing*

file:///home/roblaing/ebooks/LogicForProblemSolving.pdf

resolution rule

convert from standard from to clausal form

# Logic

30/50

http://infolab.stanford.edu/~ullman/focs/ch12.pdf

## DeMorgan’s Laws

¬(p ∧ q) ⇔ ¬p ∨ ¬q ¬(p ∨ q) ⇔ ¬p ∧ ¬q

Truth tables 12.4

Converting truth tables to logical expressions 12.5

Karnaugh maps 12.6

Logical expressions 12.7, 12.8

Common proof techniques 12.9

Deduction 12.10

Resolution 12.11

# Sets

http://infolab.stanford.edu/~ullman/focs/ch07.pdf

Stephen Cole Kleene Mathematical Logic

*prime formulas*or*atoms*- Denoted by capital Roman letters from late in the alphabet, as P, Q, R, …, P
_{1}, P_{2}, P_{3}, … *composite formulas*or*molecules*- These consist of five rules.

- Equivalence ⇔, ≡, ↔, ~
- Implication ⇒, →, ⊃
- Conjuction ∧, ·, & , “,”, ‘and’
- Disjunction ∨, |, “;”, ‘or’
- Negation ¬, ˜, !, “+”, ‘not’

The above order is the precedence (bottom up, with ¬ highest).

I’m opting for the same choice of symbols as

## Truth Tables

A | B | A ⇔ B | A ⇒ B | A ∧ B | A ∨ B | ¬A |
---|---|---|---|---|---|---|

t | t | t | t | t | t | f |

t | f | f | f | f | t | f |

f | t | f | t | f | t | t |

f | f | t | t | f | f | t |

*preclusion*- Possibly a better name for A ⇒ B than implication is preclusion. ¬A ∨ B gives the same truth table

Logic textbooks, eg Clarence Irving Lewis,

created a distinction between what is generally thought of as implication and the odd truth table version. Furthermore, A ⇒ B can be substituted with ¬A ∨ B.

Similarly A ⇔ B can be substituted (A ∧ B) ∨ (¬A ∧ ¬B), so ¬, ∨, ∧ are all we really need.

https://www.finophd.eu/wp-content/uploads/2018/11/Russell-Principles-of-Mathematics.pdf