Презентация, доклад по математике на тему : Множества и подмножества

mathematic’s terms and their translations.

In mathematics:
The student will be able to:
- Define set, inclusive, element, object, and roster notation.
- Identify the elements of a given set.
- Describe conventions used to list sets.
- List the elements of a set using roster notation.
- List the elements of a set by describing the set and the rules that its elements follows.
- Recognize when to describe a set and its elements instead of listing it in roster notation.
- Apply basic set concepts to complete five exercises.

She whispered to Angie that she had just bought a set of winter clothes. The outerwear collection includes a coat, a hat, a scarf, gloves, and boots. Their teacher, Mrs. Glosser, overheard the conversation and asked them: What is a set?
Solution: Luckily for Kyesha and Angie, their classmate Eduardo had a math dictionary with him! He quickly looked up the word "set" and defined it for the class as shown below.

a rule. The objects in the set are
called its elements. Set notation uses curly braces,with
elements separated by commas.

So the set of outwear for Kyesha would be listed
as follows: A = {coat, hat, scarf, gloves, boot} ,
where A is the name of the set, and the braces indicate
that the objects written between them belong to the
set.

The same object cannot be included in the set more than once.

the set of all fingers?

Solution: P = {thumb, index, middle, ring, little}
Note that there are others names for these fingers: The index finger is commonly referred to as the pointer finger; the ring finger is also known as the fourth finger, and the little finger is often referred to as the pinky. Thus, we could have listed the set of fingers as:
P = {thumb, pointer, middle, fourth, pinky}

between 0 and 10?

Solution: Q = {2, 4, 6, 8}
Note that the use of the word between means that the range of numbers given is not inclusive. As a result, the numbers 0 and 10 are not listed as elements in this set.

this on the chalkboard: In fine arts, primary colors are sets of colors that can be combined to make a useful range of colors. Then she asked the class: What is the set of primary colors?
Solution: Eduardo answered: red, blue and yellow. Angie answered: We can use set notation to list the set of all primary colors. Kyesha went to the chalkboard and wrote:
X = {red, blue, yellow}


The teacher said: Good work everyone. This is a nice combination of art and math!

of elements, and each element within a set was unique. In these examples, certain conventions were used.

The following conventions are used with sets:
Capital letters are used to denote sets.
Lowercase letters are used to denote elements of sets.
Curly braces { } denote a list of elements in a set.

follows:
A = {coat, hat, scarf, gloves, boots}
P = {thumb, index, middle, ring, little}
Q = {2, 4, 6, 8}
X = {red, blue, yellow}

a list of elements, separated by commas, enclosed in curly braces. The curly braces are used to indicate that the elements written between them belong to that set. Let's look at some more examples of sets listed with roster notation.

the English alphabet.
Solution: R = {a, e, i, o, u}

Example 6:Let G be the set of all whole numbers less than ten.
Solution: G = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Example 7:Let T be the set of all days in a week.
Solution: T = {Monday, Tuesday, Wednesday, Thursday, Friday}

Example 8:Let X be the set of odd numbers less than 12.
Solution: X = {1, 3, 5, 7, 9, 11}

Example 9: Let Y be the set of all continents of the world.
Solution: Y = {Asia, Africa, North America, South America, Antarctica, Europe, Australia}

the elements of a set. In this case, it is better to describe the set. The rule that the elements follow can be given in the braces. For example: R = {vowels} means Let R be the set of all vowels in the English alphabet.
This is especially useful when working with large sets, as shown below.

= {prime numbers less than 100}
M = {state capitals in the US}

element in that set. Thus, there are two methods for indicating a set of objects:
listing the elements;
2) describing the elements.

11 below.

Example 10: What is the set of all letters in the English alphabet?

Listing elements: D = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}
Describing elements: D = {letters in the English alphabet}

Example 11: What is the set of all states in the Unites States?
Solution: R = {all states in the US}

easier to describe its elements than to list them.
Similarly, in example 11, set R has 50 elements, so it is easier to describe its elements.

common or follow a rule.
The objects in the set are called its elements. 
Set theory is the branch of mathematics that studies sets, which are collections.
Set notation is a precise way of describing which items belong in a set and which do not. Specific symbols are used in set notation. of objects.
An inclusive range of numbers includes the first and last number and all numbers in between.
Roster notation is a list of elements, separated by commas, enclosed in curly braces.

a standard deck of playing cards?  a) R = [ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, king].  b) S = {hearts, diamonds, clubs, spades}.  c)T = {jokers}.  d)None of the above.

ANSWER: b)

less than 10?  a) C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.  b) D = {0, 2, 4, 6, 8}.  c) E = {1, 3, 5, 7, 9}.  d) None of the above.

ANSWER: c)

earth? a)  G = {Atlantic, Pacific, Arctic, Indian, Antarctic}.  b) E = {Amazon, Nile, Mississippi, Rio Grande, Niagara}.  c) F = {Asia, Africa, North America, South America, Antarctica, Europe, Australia}.  d) All of the above.

ANSWER: a)

matter? a)  X = {iron, aluminum, nickel, copper, gold, silver}.  b) Y = {hydrogen, oxygen, nitrogen, carbon dioxide}.  c) Z = {liquids, solids, gases, plasmas}.  d) None of the above.

ANSWER: c)

‘library’ as shown below. What is wrong with this set? A = {l, i, b, r, a, r, y} a) A capital letter is used to represent this set. b)  It uses curly braces. c) It uses commas. d)The objects in this set are not unique.

ANSWER: d)