Draw another Venn diagram that shows the result

Assignment Help Mathematics

Reference no: EM133568623 , Length: 10 pages

MATHEMATICS FOR IT

QUESTION 1

Suppose that the Mathematics class comprises the following students:

Name	Age
Afiq	26
Amni	39
Fakhrul	36
Faris	38
Amirul	44
Hani	34

(a) Write a set A that contains the name of students whose age is between 20 to 37.

(b) Write a set B that contains the name of students that become the complement of set A above.

The following questions are based on set A and set B that you have obtained from question (a) and (b)
(c) Determine the cardinality of set A and set B above.
(d) Write the power set of set A and set B above.
(e) Draw a Venn diagram that contains set A and set B above.
(f) Write the result of set operation A ∩ B and A U B above.
(g) Draw a Venn diagram that shows the result of A ∩ B above.
(h) Draw another Venn diagram that shows the result of A U B above.
(i) Determine whether A is a subset of B.

QUESTION 2

(a) Let P(x,y) be the statement "x has met y". The domain for x and y is all students taking discrete mathematics. Translate each of the following logical expressions into a sentence:

∃x∃y·P(x,y)
∃x∀y·P(x,y)
∀x∃y·P(x,y)
∃y∀x·P(x,y)

(b) Let Q(x,y) be the statement "x likes y". The domain for x and y is the people in the world. Translate the following statements using quantifiers.

Everybody likes somebody.
There is somebody whom everybody likes.
Nobody likes everybody
There is somebody whom no one likes.

QUESTION 3

Let set A = {1, 2, 3, 4} and B = {5, 6, 7, 8} whereby relation R₁= {(a, b) | a = b - 1 } and R₂ = {(a, b) | a + b ≥ 3}. a is an element of set A and b is an element of set B.

i. Write the relation for R1 and R2 where these represent the relation from set A to set B.
ii. Based on the question in (i), solve R₁ - R2 and R2 - R1.
iii. Evaluate R₁ o R2 and R2 o R1.
iv. Suppose R₃ is a relation on the same set A, write the relation R3 = {(a, b) | a mod b = 1 }.
v. Determine whether the relation R₃ is reflexive, symmetric, anti-symmetric and transitive.
vi. Determine whether the relation R₃ is an equivalence relation or partial order. Give reason for your answer.

Reference no: EM133568623

Questions Cloud

Explain how you would use theory in your counseling practice : Theories are used to inform counselors of ethical practices. Explain how you would use this theory in your counseling practice to support individuals in crisis.

What are the most important ways that the triangle fire : what are the most important ways that the Triangle Fire influenced modern social policy? Are modern labor laws still necessary? Are there any changes you would

Describe social psychological theory and research : Describe social psychological theory and research that explains these principles. Discern applicable theory regarding social relations and principles

Explain the role of women during the era : Explain the role of women during this era. How was women's involvement during this time a precursor to the development of the social work profession?

Draw another Venn diagram that shows the result : CDMA2103 MATHEMATICS FOR IT, Open University Malaysia - Draw a Venn diagram that contains set A and set B above. (f) Write the result of set operation

Describe how social welfare agencies discriminated : Describe how social welfare agencies discriminated against African Americans and how these same systems may still oppress them.

Explain patterns of attachment and give example of each one : Explain four patterns of attachment and give an example of each one. Indicate which pattern you find to be the most common, and support your answer with example

How might these societal factors influence family dynamics : What are all of the societal factors involved, for each family member? How might these societal factors influence family dynamics?

Describes and represents mathematical situations : Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

User Account

All Pages