Category: Set Theory

these three questions need to be done in MATLAP app. please let me know if you want any clarification.

please read through this VERY carefully:
this assgment is a signature paper, that is mean it shoud be very precise. in this paper I have attached in this assignment document that I need to be explicated, from page 1 to 8 pdf pages. before ypu explicate page 1-8, you should copy everything on pages 1 to 8 in a word document then start explicating. Please note that, your explication should be in [squere brackets] to diffrentiate your work from the orignal text. also note that you might use (equation editor) to write the equations on the word document. , TimesNewRoman font, 12 pointsize, 1 inch marginsdouble sapce I am expecting 4000-4500words

there are three assignments. two of them needs to be done in MATLAP application.
note that homework 21 has two parts (a) and (b)
homework 23 has three parts a,b, and c and they are mathmatical problem do not need MATLAP

A detailed exploration of the stages of cognitive development in preschool children, emphasizing how these stages relate to the development of logical-mathematical concepts.
– An examination of various methodological strategies that can be used to promote mathematical understanding, explaining the justification and effectiveness of each one.
– A reflection on the challenges and successes of integrating theoretical knowledge with practical application in preschool settings, based on real-life examples or case studies.
– Recommendations for educators who seek to effectively integrate theory and practice into preschool mathematics education.

1a. Set Builder form: {x | x is a natural number and x > 4}
What is the Roster form?
1b. {14, 15, 16}
What is the set builder form?
2a. {-3, -2, -1, 0, 1, 2}
What is the set builder form?
2b. Set Builder form: {y | y is an integer and y>=-2}
What is the roster form:
3a. Let sets A and B be defined as follows.
A= {−27, −26, −25, −24, -23}
B is the set of integers greater than or equal to −5 and less than or equal to 2.
Find the cardinalities of A and B.
n (A) = and n (B) =
3b. TRUE or FALSE
-19 ∈ A
-2 ∈ B
-23 ∈ A
6 ∉ B
4. For each pair of sets, choose the best description.
(a)
A = {34, 35, 36}
B = {72, 73, 74}
*equivalent but not equal
*equal but not equivalent
*both equivalent and equal
*neither equivalent nor equal

4b. A is the set of even numbers greater than 9 and less than 17.
B = {10, 12, 14, 16} *equivalent but not equal
*equal but not equivalent
*both equivalent and equal
*neither equivalent nor equal
4c. A is the set of integers greater than 2 and less than 6.
B is the set of integers greater than 2.
*equivalent but not equal
*equal but not equivalent
*both equivalent and equal
*neither equivalent nor equal
4d. A = {f, h, j, m}
B = {j, c, g}*equivalent but not equal
*equal but not equivalent
*both equivalent and equal
*neither equivalent nor equal
Decide whether each statement is true or false.
5a. {f, h, j} ⊆ {f, h, j}
5b. {1, 4} ⊂ {1, 2, 3, 4, …}
5c. {p, q, r, s, t, u} ⊈ {p, s, u}
5d. ∅ ⊈ {12, 13, 19}
6. A jazz band has three star players: Evans, Davis, and Mingus. The director can choose to have some or none, but not all, of them play in a show. In the braces below, list all the possible sets of star players that the director can have play.
Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol ∅.
7. Let the set A be defined as follows.
A = {53,47,43,17,13,11,7,5}
a. Find the total number of subsets of A.
b. Find the total number of proper subsets of A.
8. For the universal set, U = {f, g, h, p, q}, complete the parts below. Write your answers in roster form or as ∅.
a. Suppose A = {f, h, p, q} . Then what is A′ ?
b. Suppose we know that B′ = {g, h}. Then what would B have to be?
9. Sets C And D are subsets of the universal set U. These sets are defined as follows.
U = { m, q, r, x, y }

C = { m, q }
D = { m, r, x}
Find the following sets. Write your answer in roster form or as ∅.
a. C∩D′ =
b. (C∪D)′ =
. =