Module 5. Mathematical Logic Flashcards
deals with the scientific method of judging the truth or falsity of statements
Logic
body of statements or mathematical sentences
Mathematics
important in understanding mathematics as a logical system
symbolic language
basis of all mathematic reasoning
logic
one of the first mathematicians to make a serious study of symbolic logic
Gottfried Wilhelm Leibniz (1646-1716)
Leibniz tried to advance the study of logic from a merely __ subject to a formal __ subject
- philosophical
- mathematical
Was Leibniz able to achieve the goal of advancing the study from merely a philosophical subject to a formal mathematical subject?
no
(HAHAHAHA taas kaayo question unya ani ra answer)
Several mathematicans who contributed to the advancement of symbolic logic as a mathematical discipline
- Augustus De Morgan (1806-1871)
- George Boole (1851-1864)
- declarative sentence
- either true or false
- but not both true and false
statement/proposition
To determine whether a sentence is a statement, it may not be necessary to determine whether it is __
true
a statement is either true or false but not
both true and false
statement that conveys a single idea
simple statement
statement that conveys two or more ideas
compound statement
denial of a statement
negation
if p is any proposition, what is its negation symbol
~p (not p)
negation of a true statement
false
negation of a false statement
true
truth table for negation
p ~p
T
F
p ~p
T F
F T
some, all, and no (or none)
quantifiers
examples of quantifiers
- some
- all
- no (or none)
Negation of:
all p are q
some p are not q
Negation of:
some p are q
no p are q
- if p and q denotes to propositions
- compound proposition “p and q”
conjunction of p and q
symbol of conjunction of p and q
p ∧ q