Math 1100 Chapter 2 : Lesson 3 and 4

Math as Language and Sets

Language

This is important in performing man’s everyday activities. This is commonly used to develop ideas and to express them to other people.

Precise

“Math expression has its own distinct meaning”. Which characteristic of math is being described?

Concise

“Math expression uses symbols instead of spelled-out words.” Which characteristic of math is being decribed?

Powerful

“Mathematics can only be performed efficiently if students can understand the language of mathematics.” Which characteristic of mathematics is being described?

Expression

These are considered as the correct arrangement of mathematical symbols used to represent mathematical object of interest. (DOES NOT STATE A COMPLETE THOUGHT)

verbal phrases

These are translated into variable expressions to simplify them into an equivalent form that usually involves fewer symbols and operations.

Mathematical sentence

It is a correct arrangement of mathematical symbols stating a COMPLETE THOUGHT.

Open sentence

A mathematical sentence that may be either true or false.

Closed Sentence

It is a mathematical sentence which is definitely true or definitely false.

Sets

It is a collection or groupings of elements

Capital Letters

These are usually used to name sets, if the elements are also letters, then small letters are used.

Roster (List)

A way to describe a set by listing down the elements.

Rule (Description Method)

A way to describe sets by giving a description that befits each of the elements.

Null or empty set

Any set that has no element at all

Equal or Identical

Two sets are ________ if they have the SAME ELEMENTS

Equivalent

If two sets have the SAME NUMBER of elements

Universal Set (U)

Any set that contains all elements under consideration is __________?

Union

This operation combines all elements of two sets. (basta walang mauulit na element)

Intersection

This operation contains all the elements found in two sets . (Kung ano lang ung common element sa both sets)

Complement

This operation identifies the elements of the universal set that are not in A. (yung mga wala sa may ganito — { ‘ } — ilalagay sa next set)

Difference

It is defined to be the set whose elements are those of A that are not in B.

Cartesian or Cross Product

It is the set of all ordered pairs (x,y), such that x is an element of set A and y is an element of set B. (so lahat ng possible sets of x,y is ilalagay)