mathmod

SETS

• Is a collection of distinct well-defined objects called elements.

elements

s a collection of distinct well-defined objects called

set notation

There is a fairly simple notation for sets. We simply list each element (or "member") separated by a comma, and then put some curly brackets around the whole thing

RELATION

is a set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation, the set of all the second components are called the range of the relation.

domain, range

is a set of ordered pairs. The set of all first components of the ordered pairs is called the _____ of the relation, the set of all the second components are called the ________ of the relation.

FUNCTION

is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

function

1. {(7,9), (-1,0)}

not fuction

1. {(1/2,-2), (0.5,-3), (3,-9), (-3,-11)}

is simply a rule for combining two values to create a new value. The most widely known binary operations are those learned in elementary school: addition (+), subtraction (-), multiplication (×), and division (÷) on various sets of numbers.

binary operation

A ______ _______ on a set is a calculation involving two elements of the set to produce another element of the set.

propositional logic

is a mathematical system for reasoning about propositions and how they relate to one another.

PROPOSITIONAL VARIABLES

• It is a variable that represents propositions.

propositional variables

are usually represented as lower-case letters, such as p, q, r, s, etc.

NEGATION

• ~p is true if and only if p is false

NEGATION

• Read “not p”

AND

p∧q

CONJUNCTION

• p∧q is true if both p and q are true

or

p∨q

disjunction

• p∨q is true if at least one of p or q are true

if, then

p→q

conditional

p and q might both be true; p might be true and q is false; p might be false and q is true; p and q might both be false

if and only if

p↔q

biconditional

• p and q are logically equivalent if they have identical truth values under all possible situations

QUANTIFIERS

• Are words that denote the number of objects or cases referred to in a given statement. It comes from the Latin word “quantos”. English quantifiers include “all”, “none”, “some”, and “not all”.

QUANTIFIERS

• The ______ “all”, “every”, and “each” illustrate that each and every object or case satisfies the given condition.

QUANTIFIERS

• The ________ “some”, “several”, “one of” and “part of” illustrate that not all but at least one object or case satisfies the given condition.