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# Discrete Structures

A set of discrete elements on which certain operations are defined and implies noncontinuous and therefore discrete sets include finite and countable sets.

## lab programs

Objects that can be counted are called?

• Discrete
• Infinite
• Finite
• None among the choices

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?

• Vowel Letters
• English Alphabet Letters
• Small Letters
• None of the Choices

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

• True
• False

One-to-one is not a type of function

• True
• False

Multiple Choice: Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. j2-12j+n

• n = 6; (j + 6)2
• n = 36; (j - 6)
• n = 6; (j - 6)
• n = 36; (j - 6)2
• n = 6; (j - 6)2

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

• Injective
• Surjective
• None of the choices
• Bijection

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

• Postorder
• Preorder
• None of the choices
• Inorder

It is a collection of objects called elements?

• Set
• Members
• None of the Choices
• Group

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

• {1,2,3,4}
• {1,2,3,4,x,y,z}
• None of the choices
• {x,y,z}

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?

• Descriptive
• Tabular
• Set Builder
• None of the choices

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

• Tree
• None of the choices
• Loop
• Graph

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

• 720
• 120
• 24
• 2160

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?

• 27
• 900
• 30
• 1000

Determine whether the equation is a conditional equation, an identity, or a contradiction. 5(z + 2) - 3z = -4(-(1/2)z+1) + 14

• Conditional
• Identity

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

• 4
• 7
• 5
• 6

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

• Combination
• Factorial
• Counting
• Permutation

If f : A —> B , then A is called?

• Domain of f
• Function of f
• Codomain of F
• None of the choices

A tree is not a tree if it has?

• |E| < |V|
• |E| ≥ |V| (TRY)
• |E|> |V|
• None of the choices

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

• 260
• 36
• 2600
• 26000

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

• 4
• 5
• None of the choices
• 6

Multiple Choice: Solve the Equation -5(2y + 3) + 5 = 0

• {2}
• {4}
• {1}
• {-1}
• {-4}

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

• Fuzzy Logic
• Propositional Logic
• None among the choices
• First Order Predicate Logic

It specifies the meaning of mathematical statements?

• None among the choices
• Rules of Logic
• Reason
• Logic

Solve the system by substitution. 8x - y = 1 12 + 5y = 8

• {(12, 4)}
• { }
• {(1, 7)}

Multiple Choice: Solve the Problem The sum of an integer and its square is 72. Find all possible integers.

• 8 and 64
• 64 and 81
• -9 and 81
• 8 and -9
• -8 and 9

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

• None of the Choices
• Tautology
• Proposition

It refers to statements that supports the arguments?

• Conclusions
• Propositions
• Premises
• None among the choices

If \$19,000 is borrowed at 7.1% simple interest for 10 years, how much interest will be paid for the loan?

• \$37,726.66
• \$18,726.66
• \$13,490.00
• \$32,490.00

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

• 24
• 12
• 8
• 9

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

• 1
• 3
• 0
• 2

Multiple Choice; Convert the expression to radical form and simplify 491/2

• 49/2
• 2401
• √7
• Not a Real number
• 7

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

• Spanning Tree
• Binary Tree
• None of the choices
• Rooted Tree

Multiple Choice: Solve the rational equation. 4/x + 5/2 = 7/4

• {16/3}
• {-16/3}
• {3/16}
• {-8/3}
• {-3/16}

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

• Discrete
• None among the choices
• Mathematics
• Logic

Solve the problem. The width of a rectangular is 6 ft less than 4 times the length. Write a model for the width W in terms of the length L.

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

• Height
• None of the choices
• Root
• Level

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?

• 20
• 200
• 10
• 30

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

• True
• False

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

• None of the Choices
• True
• False
• Either True or False

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

• None of the choices
• Loop
• Isolated
• Parallel

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

• Argument
• Proposition
• Statement
• None among the choices

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

• Indegree
• None of the choices
• Outdegree
• Degree

The width of a rectangle is 7 ft less than 4 times the length. Write a model for the width W in terms of the length L.

• W = 7L - 4
• W = 4L + 7
• W = 7L + 4
• W = 4L - 7
• W = 4(L - 7)

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

• None of the Choices
• Neither True or False
• True
• False

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

• None of the choices
• Level
• Height
• Node

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?

• Combination
• Permutation
• Factorial
• Counting

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

• One-to-One
• One-to-One Correspondence
• None of the choices
• Onto

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

• Law of Identity
• None among the choices
• Law of Exclude Middle

Multiple Choice; Simplify the radical 3√72

• 63√2
• 83√9
• 93√2
• 23√9
• 83√36

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?

• Indegree
• Bipartite
• None of the choices
• Subgraph

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

• 36
• 12
• 24
• 6

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

• Finite Set
• Counting Set
• Infinite Set
• None of the Choices

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

• True
• False

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?

• 16
• 2
• 8
• 32

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

• True
• False

Multiple Choice: Solve the Equation The product of two consecutive positive even integers is 120. Find the integers.

• 58 and 62
• 59 and 61
• 10 and 12
• 8 and 10
• 12 and 14

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

• 50
• 252
• 120
• 500

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

• None of the choices
• Digraph
• Graph
• Simple graph

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

• 45
• 100
• 25
• 20

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

• True
• False

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

• Mathematical Reasoning
• Algorithmic Thinking
• None among the choices
• Mathematical Modeling

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

• Power Set
• None of the choices
• Set Identity
• Set Cardinality

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

• None among the choices
• Tautology
• Proposition

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

• True
• False

Tautology is a statement that is always false

• True
• False

Multiple Choice; A tool rental store charges a flat fee of \$5.50 to rent a chain saw, and \$7.00 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

• \$12.50
• \$49.00
• \$87.50
• \$47.50
• \$54.50

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

• None among the choices
• Discrete
• Statistics
• Algebra

Refers to a vertex on which no edges are incident?

• Loop
• None of the choices
• Isolated
• Edge-Endpoint

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?

• v1
• None of the choices
• v3
• v2

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

• 120
• 125
• 25
• 100

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?

• 37
• 39
• 36
• 38

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

• 30
• 720
• 360
• 36

It is a vertex distinguishable from other vertex?

• Root
• Left Child
• Right Child
• None of the choices

It refers to statement being supported in the argument?

• Premises
• Conclusion
• Propositions
• None among the choices

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. t2-(4/3)t+n

• n=4/9 ; (t-(2/3))2
• n=4/9 ; (t+(2/3))2
• n=16/9 ; (t-(4/3))2
• n=4/9 ; (t-(2/9))2
• n=8/9 ; (t-(8/9))2

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

• English Alphabet Letter
• Small Letters
• Vowel Letters
• None of the Choices

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

• Identity Law
• De Morgan's Law
• None of the Choices
• Idempotent Law

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?

• 45
• 6
• 10
• 19

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

• True
• False

Contradiction is a statement that is always true

• True
• False

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?

• 8
• 13
• 6
• 1

Multiple Choice; Simplify the radical. Assume that all variables represent positive real numbers.

• 3z√7z3
• 9z2√7z
• 3√7z5
• 3z2√7z
• 9z4√7z

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

• 210
• 252
• 50
• 30240

Vertices with the same parent are called?

• Siblings
• Child
• None of the choices
• Descendants

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

• Z
• W
• N
• None of the choices

Write the requested inequality.

• m ≤ 17
• m ≤ 16
• m ≤ 19
• m ≤ 18

It is the negation of Tautology?

• Proposition
• Tautology
• None among the choices

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?

• e2
• e3
• None of the choices
• e4

It is a connected graph that contains no cycles?

• Subgraph
• None of the choices
• Tree
• Complete Graph

It is an edge with just one endpoint?

• Edge-Endpoint
• None of the choices
• Parallel
• Loop

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?

• 1
• 2
• None of the choices
• 3

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?

• Permutation
• Counting
• Combination
• Factorial

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

• Neither True or False
• True
• None of the Choices
• False

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

• C = {x | x is an even number and x <=100}
• C = {x|x is an even number}
• C = {x|x is an integer and x<=100}
• None of the choices

Simplify

• 1/16
• -1/16
• 0
• 1
• -1

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

• 34
• 12
• 4
• None of the choices

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

• 4
• None of the choices
• 6
• 5