Discrete Structures 1

Discrete Structures 1

Question 1

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In how many ways can 5 different books be arranged on a shelf?

Select one:

a.

120

b.

125

c.

100

d.

25

Question 2

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Refers to the sum of the indegree and outdegree of the graph?

Select one:

a.

Indegree

b.

None of the choices

c.

Outdegree

d.

Degree

Question 3

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Refers to a vertex on which no edges are incident?

Select one:

a.

Loop

b.

None of the choices

c.

Isolated

d.

Edge-Endpoint

Question 4

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How many edges can fully connect a graph with 4 vertices?

Select one:

a.

4

b.

5

c.

None of the choices

d.

6

Question 5

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Given the set of four letters, {A, B, C, D}, how many possibilities are there for selecting any two letters where order is important?

Select one:

a.

12

b.

24

c.

8

d.

9

Question 6

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It refers to the number of ways in which a subset of objects can be selected from a given set of objects, where order is not important?

Select one:

a.

Permutation

b.

Counting

c.

Combination

d.

Factorial

Question 7

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A tree is not a tree if it has?

Select one:

a.

|E| < |V|

b.

|E| ≥ |V| (TRY)

c.

|E|> |V|

d.

None of the choices

Question 8

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If A=6!, then A is equal to?

Select one:

a.

360

b.

720

c.

36

d.

30

Question 9

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Vertices with the same parent are called?

Select one:

a.

Descendants

b.

Child

c.

Siblings

d.

None of the choices

Question 10

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It consists of two finite sets, a nonempty set V(G) of vertices and a set E(G) of edges?

Select one:

a.

Tree

b.

None of the choices

c.

Loop

d.

Graph

Question 11

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The Gilas Pilipinas Basketball Team has 10 players. How many ways can the coach select 5 players to start the game?

Select one:

a.

50

b.

30240

c.

210

d.

252

Question 12

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In a graph, let V = {v1, v2, v3, v4}, and E = {e1, e2, e3, e4}, assuming the endpoints of e1are v1 and v2, the endpoints of e2 are v1 and v3, the endpoints of e3 are v2 and v3, theendpoint of e4 is v4. What is the loop in the graph?

Select one:

a.

e2

b.

e3

c.

None of the choices

d.

e4

Question 13

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A computer password consists of a letter of the alphabet followed by three digits. Find the total number of passwords that can be created.

Select one:

a.

260

b.

36

c.

2600

d.

26000

Question 14

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Among 366 people, at least how many people could have the same birthday?

Select one:

a.

1

b.

3

c.

0

d.

2

Question 15

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How many bit strings of length 4 contain either 3 consecutive 0s or 3 consecutive 1s?

Select one:

a.

4

b.

7

c.

5

d.

6

Question 16

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A standard deck of playing cards consist of 52 cards, 4 suits for each 13 cards. How many ways can you choose 2 kings from 4 available kings suits?

Select one:

a.

8

b.

13

c.

6

d.

1

Question 17

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Refers to a graph that does not have any loops or parallel edges?

Select one:

a.

None of the choices

b.

Digraph

c.

Graph

d.

Simple graph

Question 18

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It is a complete Graph where each vertex in one of the subsets is connected by exactly one edge to each vertex in the other subset, but not to any vertices in its own subset?

Select one:

a.

Indegree

b.

Bipartite

c.

None of the choices

d.

Subgraph

Question 19

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In a graph, let V = {v1, v2, v3}, and E = {e1, e2, e3}, assuming the endpoints of e1 are v1and v2, the endpoints of e2 are v1 and v3, the endpoints of e3 are v2 and v3. Then e1 and e2 are incident on what vertex in the graph?

Select one:

a.

v1

b.

None of the choices

c.

v3

d.

v2

Question 20

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A tree traversal where the left subtree is visited first, followed by the root, then the right subtree?

Select one:

a.

Postorder

b.

Preorder

c.

None of the choices

d.

Inorder

Question 21

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It is the number of edges along the unique path between it and the root?

Select one:

a.

Node

b.

Level

c.

None of the choices

d.

Height

Question 22

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It is defined to be the product of all the integers from 1 to n and is denoted n!?

Select one:

a.

Combination

b.

Factorial

c.

Counting

d.

Permutation

Question 23

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It is an edge with just one endpoint?

Select one:

a.

Loop

b.

Edge-Endpoint

c.

Parallel

d.

None of the choices

Question 24

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If 75 students are to be assigned in a room, filling all available rooms, how many rooms would require two students to share a room? 

Select one:

a.

37

b.

39

c.

36

d.

38

Question 25

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It is the maximum level of any vertex of the tree?

Select one:

a.

Height

b.

Level

c.

Root

d.

None of the choices

Question 26

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A local telephone number in an office is given by a sequence of three digits. How manydifferent telephone numbers are there if the first digit cannot be 0?

Select one:

a.

27

b.

900

c.

30

d.

1000

Question 27

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In how many ways can you choose 5 out of 10 friends to invite to a dinner party?

Select one:

a.

50

b.

252

c.

120

d.

500

Question 28

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It refers to the number of ways in which a subset of objects can be selected from a given set of objects, where order is important?

Select one:

a.

Combination

b.

Permutation

c.

Factorial

d.

Counting

Question 29

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A circuit can store a bit, a binary digit, 1 or 0. So, for 1 bit, there are 2 possible states.How many possible states if the binary has 4 bits?

Select one:

a.

16

b.

2

c.

8

d.

32

Question 30

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Given a graph with V = {a, b, c, d}, and E = {(a, b), (a, c), (b, c) (c, d), (b, d)}, how manyedges should be deleted to create a spanning tree?

Select one:

a.

1

b.

2

c.

None of the choices

d.

3

Question 31

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Refers to a vertex unconnected by an edge to any other vertex in the graph?

Select one:

a.

None of the choices

b.

Loop

c.

Isolated

d.

Parallel

Question 32

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If there are 20 girls and 10 boys in the class and you want to speak to one student of theclass. How many choices do you have?

Select one:

a.

20

b.

200

c.

10

d.

30

Question 33

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Two dice are thrown. How many possible outcomes are there?

Select one:

a.

12

b.

36

c.

24

d.

6

Question 34

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35 voters were surveyed about their opinions regarding two presidentiables. 16supported presidentiable 1 and 29 supported presidentiable 2. How many voters supported both, assuming that every voter supported either presidentiable 1 or presidentiable 2 or both?

Select one:

a.

45

b.

6

c.

10

d.

19

Question 35

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It is a vertex distinguishable from other vertex?

Select one:

a.

Root

b.

Left Child

c.

Right Child

d.

None of the choices

Question 36

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It is a tree in which there is one vertex that is distinguished from the others?

Select one:

a.

Spanning Tree

b.

Binary Tree

c.

None of the choices

d.

Rooted Tree

Question 37

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It is a connected graph that contains no cycles?

Select one:

a.

Complete Graph

b.

None of the choices

c.

Subgraph

d.

Tree

Question 38

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There are 20 CS majors and 25 IT majors. How many ways are there to pick one CS major or one IT major?

Select one:

a.

45

b.

100

c.

25

d.

20

Question 39

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A graph having 6 vertices and 9 edges, if a tree is to make from a graph, how many edges should be deleted?

Select one:

a.

4

b.

None of the choices

c.

6

d.

5

Question 40

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In how many different ways can the letters of the word 'DISCRETE' be arranged in such away that the vowels always come together?

Select one:

a.

720

b.

120

c.

24

d.

2160

Question 1

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 If f : A —> B , then A is called?

Select one:

a.

Function of f

b.

None of the choices

c.

Codomain of F

d.

Domain of f

Question 2

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A function f:A→B is a one-to-one correspondence, or a bijection

Select one:

True

False

Question 3

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Functions are also used represent how long it takes a computer to solve problems of a given size.

Select one:

True

False

Question 4

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In many instances, we assign to each element of a set a particular element of a second set.

Select one:

True

False

Question 5

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It is a type of function where two distinct elements of A do not map to the same element of B?

Select one:

a.

One-to-One

b.

One-to-One Correspondence

c.

None of the choices

d.

Onto

Question 6

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A function f:A→B is called onto, or injunction

Select one:

True

False

Question 7

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One-to-one is not a type of function

Select one:

True

False

Question 8

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Let A = {1, 2, 3, 4} and B = {x, y, z}, if f:A—>B, then the domain of f is?

Select one:

a.

{x,y,z}

b.

{1,2,3,4}

c.

None of the choices

d.

{1,2,3,4,x,y,z}

Question 9

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If f:A->A, and f(A)=3x, then f(4)?

Select one:

a.

34

b.

12

c.

None of the choices

d.

4

Question 10

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It is a type of function that is both one-to-one and onto?

Select one:

a.

Injective

b.

Surjective

c.

None of the choices

d.

Bijection

Question 1

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It is a set representation where all the elements in the set are all listed separated by commas and enclosed within braces or curly brackets?

Select one:

a.

Descriptive

b.

Tabular

c.

Set Builder

d.

None of the choices

Question 2

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The ordering of elements in a set is insignificant and may contain duplicates.

Select one:

a.

None of the Choices

b.

True

c.

False

d.

Either True or False

Question 3

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A = {a, e, i, o, u} is a set of?

Select one:

a.

English Alphabet Letter

b.

Small Letters

c.

Vowel Letters

d.

None of the Choices

Question 4

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It refers to an equation that is universally true for all elements in some set?

Select one:

a.

Power Set

b.

None of the choices

c.

Set Identity

d.

Set Cardinality

Question 5

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It is a collection of objects called elements?

Select one:

a.

Set

b.

None of the Choices

c.

Group

d.

Members

Question 6

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The elements of a set must be distinct, ordered and well-defined?

Select one:

a.

Neither True or False

b.

True

c.

None of the Choices

d.

False

Question 7

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Represent C={2, 4, 6, 8, 10, …, 100} using Set Builder Form.

Select one:

a.

None of the choices

b.

C = {x|x is an integer and x<=100}

c.

C = {x|x is an even number} 

d.

C = {x | x is an even number and x <=100}

Question 8

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The Set of Natural Numbers is represented using the boldface letter?

Select one:

a.

Z

b.

W

c.

N

d.

None of the choices

Question 9

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 If the elements of the set cannot be counted or enumerated, then the set is said to be?

Select one:

a.

Finite Set

b.

Counting Set

c.

Infinite Set

d.

None of the Choices

Question 10

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 B = {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z} is a set of?

Select one:

a.

Vowel Letters

b.

English Alphabet Letters

c.

Small Letters

d.

None of the Choices

Question 1

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Using Identity Law, the proposition p V False is equivalent to?

Select one:

a.

None of the Choices

b.

Neither True or False

c.

True

d.

False

Question 2

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It is that part of logic which deals with statements that are either true or false but not both?

Select one:

a.

Fuzzy Logic

b.

Propositional Logic

c.

None among the choices

d.

First Order Predicate Logic

Question 3

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Contradiction is a statement that is always true

Select one:

True

False

Question 4

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It is the study of the methods and principles used to distinguish good (correct) from bad(incorrect) reasoning?

Select one:

a.

Discrete

b.

None among the choices

c.

Mathematics

d.

Logic

Question 5

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It is the Law of Aristotelian Logic which states that “No Statement is both true and false”?

Select one:

a.

Law of Identity

b.

None among the choices

c.

Law of Exclude Middle

d.

Law of Non-contradiction

Question 6

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It exists if and only if the two propositions have identical truth values for each possible substitution of propositions for their proposition variable?

Select one:

a.

None of the Choices

b.

Contradiction

c.

Tautology

d.

Proposition

Question 7

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 It is the negation of Tautology?

Select one:

a.

Proposition

b.

Contradiction

c.

Tautology

d.

None among the choices

Question 8

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Tautology is a statement that is always false

Select one:

True

False

Question 9

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It refers to statement being supported in the argument?

Select one:

a.

Premises

b.

Conclusion

c.

Propositions

d.

None among the choices

Question 10

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It is the part of mathematics devoted to the study of discrete objects?

Select one:

a.

None among the choices

b.

Discrete 

c.

Statistics

d.

Algebra

Question 11

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De Morgan's laws state that: The negation of a proposition is logically equivalent to the proposition in which each component is negated

Select one:

True

False

Question 12

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It refers to the ability to understand and create mathematical arguments?

Select one:

a.

Mathematical Modeling

b.

Mathematical Reasoning

c.

Algorithmic Thinking

d.

None among the choices

Question 13

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It refers to statements that supports the arguments?

Select one:

a.

Conclusions

b.

Propositions

c.

Premises

d.

None among the choices

Question 14

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It specifies the meaning of mathematical statements?

Select one:

a.

None among the choices

b.

Rules of Logic

c.

Reason

d.

Logic

Question 15

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It is a group of propositions/statements which is divided into one or more premises and one and only one conclusion?

Select one:

a.

Argument

b.

Proposition

c.

Statement

d.

None among the choices

Question 16

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A proposition whose form is a tautology is called a tautological proposition

Select one:

True

False

Question 17

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It is the Law of Logic which states that the proposition form p Λ True ≡ p?

Select one:

a.

Identity Law

b.

De Morgan's Law

c.

None of the Choices

d.

Idempotent Law

Question 18

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A proposition whose form is a contradiction is called a tautological proposition

Select one:

True

False

Question 19

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It is a statement that is always true regardless of the truth values of the individual logical variables?

Select one:

a.

None among the choices

b.

Tautology

c.

Proposition

d.

Contradiction

Question 20

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Objects that can be counted are called?

Select one:

a.

Discrete

b.

Infinite

c.

Finite

d.

None among the choices

Question 1

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It exists if and only if the two propositions have identical truth values for each possible substitution of propositions for their proposition variable?

Select one:

a.

Contradiction

b.

Proposition

c.

Tautology

d.

None of the Choices

Question 2

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It is a statement that is always true regardless of the truth values of the individual logical variables?

Select one:

a.

None among the choices

b.

Contradiction

c.

Proposition

d.

Tautology

Question 3

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 It is the negation of Tautology?

Select one:

a.

None among the choices

b.

Proposition

c.

Tautology

d.

Contradiction

Question 4

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It is the Law of Logic which states that the proposition form p Λ True ≡ p?

Select one:

a.

None of the Choices

b.

De Morgan's Law

c.

Idempotent Law

d.

Identity Law

Question 5

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Tautology is a statement that is always false

Select one:

True

False

Question 6

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Question text

Contradiction is a statement that is always true

Select one:

True

False

Question 7

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Question text

De Morgan's laws state that: The negation of a proposition is logically equivalent to the proposition in which each component is negated

Select one:

True

False

Question 8

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A proposition whose form is a contradiction is called a tautological proposition

Select one:

True

False

Question 9

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Question text

A proposition whose form is a tautology is called a tautological proposition

Select one:

True

False

Question 10

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Using Identity Law, the proposition p V False is equivalent to?

Select one:

a.

Neither True or False

b.

None of the Choices

c.

True

d.

False

Question 1

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It refers to statement being supported in the argument?

Select one:

a.

None among the choices

b.

Conclusion

c.

Premises

d.

Propositions

Question 2

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It is the study of the methods and principles used to distinguish good (correct) from bad(incorrect) reasoning?

Select one:

a.

Discrete

b.

None among the choices

c.

Mathematics

d.

Logic

Question 3

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It specifies the meaning of mathematical statements?

Select one:

a.

Rules of Logic

b.

Reason

c.

Logic

d.

None among the choices

Question 4

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It refers to the ability to understand and create mathematical arguments?

Select one:

a.

Mathematical Reasoning

b.

Mathematical Modeling

c.

Algorithmic Thinking

d.

None among the choices

Question 5

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It is that part of logic which deals with statements that are either true or false but not both?

Select one:

a.

First Order Predicate Logic

b.

Fuzzy Logic

c.

None among the choices

d.

Propositional Logic

Question 6

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It refers to statements that supports the arguments?

Select one:

a.

Propositions

b.

Conclusions

c.

None among the choices

d.

Premises

Question 7

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It is the part of mathematics devoted to the study of discrete objects?

Select one:

a.

None among the choices

b.

Algebra

c.

Statistics

d.

Discrete 

Question 8

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It is a group of propositions/statements which is divided into one or more premises and one and only one conclusion?

Select one:

a.

Argument

b.

Proposition

c.

Statement

d.

None among the choices

Question 9

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It is the Law of Aristotelian Logic which states that “No Statement is both true and false”?

Select one:

a.

Law of Exclude Middle

b.

Law of Identity

c.

Law of Non-contradiction

d.

None among the choices

Question 10

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Objects that can be counted are called?

Select one:

a.

Infinite

b.

Finite

c.

None among the choices

d.

Discrete