Math

Variables

Translate each of the following into mathematical expression.

1. The square of a number, x2

2. Four times the square of a number, 4×2

3. The product of two numbers, xy

Variable

- A symbol for a value that we don’t know yet.

- It is presented by any letter, like x and y

x, y, c, d, a, b, h, t, f, g, h

- plus

- the sum of

- increased by

- more than

- added to

ADDITION (KEYWORDS)

minus

the difference of

subtracted from

decreased by

less than

SUBTRAC

SUBTRACTION (KEYWORDS)

• times

• the product of

MULTIPLICATION (KEYWORDS)

• divided by

• the quotient of

• the ratio of

• divided into

DIVISION

SET

• A formal mathematical term introduced by Georg Cantor in 1879.

• It is a well-defined collection of distinct objects.

• It is usually represented by capital letters.

1. Universal set

2. Subset

3. Finite set

4. Infinite set

5. Empty set

6. Equal sets

7. Equivalent sets

8. Joint sets

9. Disjoint sets

9 TYPES OF SETS

Universal set

refers to all sets under investigation that are assumed to be contained in some large fixed set, which we denote by U.

Subset

is a set taken from another set.

Finite set

 is a set consisting of elements in which the number of elements is countable.

Infinite set

is a set consisting of elements in which the number of elements is NOT countable or indefinite.

Empty set

is a set that contains no elements.

can be name using { } or ∅. An empty set is also called a null set.

Equal sets

are set with exactly the same elements and cardinality.

Equivalent sets

are set with the same number of elements or cardinality.

Joint sets

• are set with common elements (intersection).

sets share at least one common element

Disjoint sets

are set with no common elements.

SET- ROSTER NOTATION

SET- BUILDER NOTATION

2 WAYS OF WRITING SETS

SET- ROSTER NOTATION

simply list each element (or member) separated by comma, then put them inside some curly brackets or braces

SET- BUILDER NOTATION

used to express a set that is defined by a logical formula that simplifies to be true for each element of the set.

SUBSET

- If A and B are sets, then A is called a subset of B, written A⊆B, if and only if every element of A is also an element of B.

Symbolically, A⊆B means that for all elements x, if x∈ A then x∈ B

PROPER SUBSET

- Let A and B are sets. A is a proper subset of B, if and only if, every element of B is in B but there is at least one element of B that is not in A.

CARTESIAN PRODUCT

- Given sets A and B, the Cartesian product of A and B, denoted by AxB, is the set of all ordered pairs (a, b), where a is in A and b is in B.

Symbolically, AxB = { (a, b)|a ∈ A and b ∈ B}