Discrete mathematics

Open Ended

Give another example the implementation discrete mathematics in informatics

Poll

As a customer of a well-known minimarket, you get a lucky draw coupon.

The lucky draw coupon can be exchanged for one of 4 alternative prizes.

If the convenience store's customers are 5000 people, what should you do

with the lucky draw coupons you have?

• 1) Entered into the lottery a luxury car (1 unit available)

• 2) An automatic motorbike will be entered into the draw (10 units available)

• 3) Entered into the drawing credit voucher worth IDR 100,000 (100 units

  available)

• 4) Exchange directly for a beautiful plate (unlimited number)

Multiple Choice

For example

A = food set ➔

{ s = soup, g = gado-gado, n = fried rice, m = boiled noodles }

B = set of drinks ➔

{ c = coca-cola, t = tea, d = dawet ice }

How many food and drink combinations can be made from the

two sets above?

• 4

• 6

• 8

• 12

Null Set

The set with the number of members = 0 is called the empty set (null set) Notation : ∅ or { }.
Example:

(i) E = { x | x < x }, then n(E) = 0

(ii) P = { Indonesians who have been to the moon }, then n(P) = 0

(iii) A = {x | x is the root of the quadratic equation x2 + 1 = 0 }, n(A) = 0

•the set {{ }} can also be written as { }

•the set {{ }, {{ }}} can also be written as {∅ , {∅}}

•{∅} is not the empty set because it contains one element, namely th

empty set.

Multiple Choice

Given a set of engineering students consisting of computer science students (300), civil engineering (400), electrical engineering (400), architecture (150), mechanical engineering (200), and industrial engineering (150),
how many members are there in the engineering student set?

• 1

• 6

• 1600

Multiple Choice

Let A = {1, 2, 3} and B = {1, 2, 3, 4, 5}.

Determine all possible sets C such that A < C and C < B,

that is, A is a proper subset of C and C is a

proper subset of B.

• {1,2,3,4} and {1,2,3,5}

• {1,2,3,4} or {1,2,3,5}

• {1,2,3,4},{1,2,3,5}

Multiple Select

Let A={a,b} and B={a,b,c,d}.

Determine all possible sets C such that A⊂C⊂B, meaning that A is a proper subset of C and C is a proper subset of B.

• {a,b,c}

• {a,b,d}

• {a,b,c,d}

• {b,c,d}

Power set

(power set) of set A is a set

whose elements are all subsets of A,

including the empty set and the set A itself.

• Notation : P(A) or 2^A

• If |A| = m, then |P(A)| = 2^m.

Example:

➢ If A = { 1, 2 }, then P(A) = { ∅, { 1 }, { 2 }, { 1, 2 }}

➢ The power set of the empty set is P(∅) = {∅}, and the power set of the set {∅} is P({∅}) = {∅, {∅}}.

Multiple Select

If A= {1,2,3}, Which one is not the member P(A)...

• 1,2,3

• {1,2,3}

• {2,3}

• 3

Multiple Select

If C={x,y,z} which of the following is not an element of P(C)?

• {x,y}

• x

• {z}

• ∅

Thank You

"Empty your cup so it can be filled; be empty so you can be full"-Bruce Lee

Multiple Choice

State the notation for the following statements:

A = the set of all domestically made cars

B = set of all imported cars

C = the set of all cars made before 1990

D = the set of all cars whose sales value is less than IDR 100 million

E = set of all cars belonging to a particular university student

Student cars produced domestically or imported from abroad

• (E∩A)∩(E∩B)

• (E∩A)∪(E∩B)

• (E∩A)

• (E∩B)

Multiple Choice

State the notation for the following statements:

A = the set of all domestically made cars

B = set of all imported cars

C = the set of all cars made before 1990

D = the set of all cars whose sales value is less than IDR 100 million

E = set of all cars belonging to a particular university student

Domestic production cars made before the year 1990 with a

sale value of less than Rp. 100 million

• C∩D∩B

• C̅∩D̅∩A

• A∩C∩D

• A∩C∪D

Multiple Choice

State the notation for the following statements:

A = the set of all domestically made cars

B = set of all imported cars

C = the set of all cars made before 1990

D = the set of all cars whose sales value is less than IDR 100 million

E = set of all cars belonging to a particular university student

Imported cars made after 1990 which have a sale value

more than IDR 100 million

• C̅∩D̅∩B

• C̅∪D̅∩B

• C̅∩D∩B

• C̅∩D∪B

Multiple Choice

Express set notation for the following statements.

U = student association

P = the set of students whose UTS test scores are above 80

Q = the set of students whose final exam scores are above 80

A student gets an A if both the UTS and UAS scores are above 80, a B if one exam is above 80, and a C if both exams are under 80.

(i) "All students who get an A"

• P∩Q

• U∪P∩Q

• U∩P∪Q

• U∩P

Multiple Choice

Express set notation for the following statements.

U = student association

P = the set of students whose UTS test scores are above 80

Q = the set of students whose final exam scores are above 80

A student gets an A if both the UTS and UAS scores are above 80, a B if one exam is above 80, and a C if both exams are under 80.

(ii) “All students who get grade B”

• U∩P∩Q

• P∩Q

• P⊕Q

• U∩P

Multiple Choice

Express set notation for the following statements.

U = student association

P = the set of students whose UTS test scores are above 80

Q = the set of students whose final exam scores are above 80

A student gets an A if both the UTS and UAS scores are above 80, a B if one exam is above 80, and a C if both exams are under 80.

(iii) “All students who get a grade of C”

• P∩Q̅

• U-(P∩Q)

• P∩Q̅

• U-(P∪Q)

Multiple Choice

Dual of (A ∩ B) ∪ (A ∩ B̅) = A

• (A ∪ B) ∩ (A ∪ B̅) = B

• (A ∪ B) ∩ (A ∪ B̅) = A

• (A ∪ B) ∩ (A ∪ B) = A

• (A̅ ∪ B̅) ∩ (A̅ ∪ B) = A̅

Open Ended

IF SET MEMBER IS D, E, F, G, what is the value of :

|D ∪ E ∪ F ∪ G|