math def Flashcards
science of correct thinking and reasoning
LOGIC
an interdisciplinary field which studies truth
and reasoning
LOGIC
(1815-1864): English mathematician and
Father of symbolic logic
George Boole
(1832-1898): English writer
and “mathematician” known as Lewis Carroll who wrote
nonsensical classics such as Alice Adventures in
Wonderland Through the Looking Glass
Charles Lutwidge Dodgson
Uses of Logic
Lawyers and judges
Programmers
Mathematicians
It is a declarative sentence that is
either true or false, but not both.
STATEMENT
It is a proposition/statement
that conveys a single idea
SIMPLE STATEMENT
It is a proposition/statement
that conveys two or more
ideas
COMPOUND STATEMENT
used several symbols to represent simple statements and connectives
George Boole
The truth value of a simple statement is
either true (T) or false (F).
The truth value of a compound statement
depends on the
truth values of its simple
statements and its connectives.
It is a collection of related and well-defined objects
called elements (denoted by ∈).
SET
(1845-1918) introduced the word set in 1879.
Georg Cantor
It is collection of all elements of all the
related sets, known as its subsets. The
universal set is usually denoted by U
UNIVERSAL SET
Symbol
ℝ
real numbers
Symbol
ℚ
rational number
Symbol
ℤ
integers
Symbol
ℕ
natural numbers
Symbol
W
whole numbers
Roster Notation
is a way of listing the elements
separated by a comma
it is a way of representing or explaining
the properties that must satisfy by the
elements of a set
Set-Builder Notation
It is a set which contains no elements
EMPTY SET
EMPTY SET
It is a set which contains no elements. It is
usually denoted
as { } or ∅
The empty set is always considered a ___
of any set.
subset
