(Sets and Subsets)

A different look at circles Set A Set B

Set C

In an excursion at Pagsanjan Falls, 80 students brought sandwiches, drinks and canned goods as follows:

• 50 students brought sandwiches• 30 students brought drinks • 30 students brought canned goods • 18 students brought canned goods and drinks• 15 students brought sandwiches and canned goods• 8 students brought sandwiches and drinks• 5 students brought sandwiches, canned goods and

drinksQuestion: How many students did NOT bring any of the 3

kinds?

SET - a well defined collection of distinct objects

- CAPITAL LETTERS are used to represents set

Example:

A = {1, 2, 3, 4, 5}

B = { M, A, T, H}

C = { all even numbers}

ELEMENT - pertains to

each object in a set

- denoted by the symbol ______ which is read as "element of set ____” while the symbol____means “NOT an element of set _____”

Example:

A ={ 1, 2, 3, 4, 5}

3 ____ of set A

7 _____ of set A

BRACES { }

- are used to enclose the elements of a given set

Example:A = { x | x is an even integer}Set is read as “the set of

all elements x, such that x is an even integer”

B = { x | x is a letter in the

word Math}

“the set of all elements of x, such that x is a letter in the word Math”

A = {x | x is a multiple of 3 between 3 and 18 }

B = { x | x is a letter in the word Algebra}

C ={ x | x is a positive odd number }

A = { 3, 6, 9, 12, 15 }

B = {A, L, G, E, B, R }

C = {1,3, 5, 7, 9, 11, 13, ….}

ROSTER/LISTING METHOD

Kinds of Sets:

FINITE SET

- a set whose number of elements can be counted

Example: A = { -1, -2, -3, -4, -

5 }

B = { x | x is a multiple of 5 between 10 and 50}

C = { x | x is a letter in the Philippine alphabet }

Kinds of Sets:

INFINITE SET

- a set whose number of elements CAN NOT be counted

Example: A = { -1, -2, -3, -4, -

5, . . . }

B = { x | x is a

multiple of 5 }

C = { x | x is a name of a person}

Kinds of Sets:

NULL / EMPTY SET

- a set that has NO element

- denoted by { } or O

Example:

A = { }

B = O

EQUIVALENT SETS

- two or more sets that have the same number of elements

Example:A = {2, 4, 6, 8,

10 }

B = { a, b, c, d, e}

Sets A and B areequivalent sets.

EQUAL SETS - two or

moresets that have

thesame

elements

Example:A = {2, 4, 6, 8,

10 }B = { 2, 4, 6, 8,

10 }

Sets A and B areequal sets.

UNIVERSAL SET

- the TOTALITY of ALL the elements in two or more given sets

- denoted by “U”

Example:

A = { 2, 4, 6, 8 }B = { 1, 2, 3, 4 } U = { 1, 2, 3, 4, 6, 8}

A = { a, b, c, d, e }B = { a, e, i, o, u } U = { a, b, c, d, e, i, o, u}

SUBSET - Set B is a

subset of Set A if and only if ALL the elements in set B is in Set A

Example:

A = { 2, 4, 6, 8 }B = { 2, 4, 8 } Set B is a subset of

Set AA = { a, b, c, d, e }B = { a, e, i, o, u } Set B is NOT a subset

of Set A