mmw module 2 1st sem prelim

Precise

it is able to make very fine distinction or definitions.

Concise or brief

if someone can say things in long exposition or sentences, mathematics can say it briefly.

Powerful

one can express complex thoughts with relatively ease.

expression

is the mathematical analogue of an English noun

Symbols

are used as part of mathematical works. It is as important as the numbers and variables that we see in mathematical expressions and sentences.

Set

well-defined collection of distinct objects.

Roster method

Listing the elements of a set and enclosing them with braces "{}"

Rule method

Describing the elements of the set. The symbol "|" is used and is read as "such that".

Finite Set

contains a countable number of elements.

Infinite Sets

counting of elements has no end.

Universal Set

The totality of elements under consideration.

Unit Set

a set with only one element.

Empty Set or null set or void set

a set containing no objects or elements

Equal set

Set A and B are equal, denoted by A = B,

Equivalent sets

If set A and B are equivalent sets, denoted by A~ B, if they have the same number of elements.

Joint Set

at least one common elements

Disjoint Sets

Sets which have no common elements

Subsets

A set whose elements are members of a given set.

Proper Subset

denoted by "A C B" if and only if ACB and A ≠ B.

Complementary Sets

two sets A and B are complementary with respect to a universal set if they are disjoint and if when combined together they form the universal set.

Power Sets

the set of all subsets (proper or not) of a set A, denoted P(A), is called the power set of A.

union

set of all elements found in A or B or both.

intersection

set of all elements common to A and B.

complement

defined as a set of elements in the universal set U that cannot be found in A.

Difference

defined as a set of elements found in A but not in B.

relation

set of ordered pairs.

domain

first elements of the ordered pairs in S.

range

second elements of the ordered pairs in S.

function

is a relation such that no two ordered pairs of the relation have the same first element.

~

negation

^

and/but

∨

or

->

implies (if, then)

<->

biconditional (if and only if)

Negation

statement obtained by negating statement

Conjunction

oining statement using the word "and"

Disjunction

formed by joining statement using the word "or".

Implication

is a conditional statement and written as "if and then" w

Biconditional

"P if and only if Q" is ca