## Discrete Structures 1

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

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

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Refers to a vertex on which no edges are incident?

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

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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?

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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?

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A tree is not a tree if it has?

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

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### Question 9

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Vertices with the same parent are called?

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

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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?

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### 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?

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### 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.

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### Question 14

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

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### Question 15

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

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### 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?

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

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### 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?

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### 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?

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### Question 20

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

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### Question 21

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

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### 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!?

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### Question 23

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It is an edge with just one endpoint?

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### 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?

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

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### 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?

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### Question 27

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

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### 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?

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### 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?

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### 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?

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### Question 31

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

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### 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?

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### Question 33

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

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### 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?

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### Question 35

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It is a vertex distinguishable from other vertex?

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### Question 36

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

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### Question 37

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It is a connected graph that contains no cycles?

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### 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?

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### 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?

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### 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?

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### Question 1

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If f : A —> B , then A is called?

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### Question 2

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

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Functions are also used represent how long it takes a computer to solve problems of a given size.
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In many instances, we assign to each element of a set a particular element of a second set.
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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?

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

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One-to-one is not a type of function
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### 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?

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### Question 9

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

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### Question 10

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

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### 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?

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

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

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

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It is a collection of objects called elements?

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

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

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### Question 8

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

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### Question 9

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

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### 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?

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### Question 1

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

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### 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?

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Contradiction is a statement that is always true
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It is the study of the methods and principles used to distinguish good (correct) from bad(incorrect) reasoning?

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

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### 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?

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It is the negation of Tautology?

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### Question 8

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Tautology is a statement that is always false
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### Question 9

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It refers to statement being supported in the argument?

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### Question 10

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

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### 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
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### Question 12

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

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### Question 13

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It refers to statements that supports the arguments?

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### Question 14

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It specifies the meaning of mathematical statements?

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### 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?

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### Question 16

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A proposition whose form is a tautology is called a tautological proposition
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### Question 17

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

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### Question 18

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A proposition whose form is a contradiction is called a tautological proposition
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### Question 19

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

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### Question 20

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Objects that can be counted are called?

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### 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?

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### Question 2

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

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It is the negation of Tautology?

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

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### Question 5

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Tautology is a statement that is always false
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### Question 6

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Contradiction is a statement that is always true
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### Question 7

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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
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### Question 8

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A proposition whose form is a contradiction is called a tautological proposition
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### Question 9

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A proposition whose form is a tautology is called a tautological proposition
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### Question 10

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

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### Question 1

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It refers to statement being supported in the argument?

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### Question 2

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

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### Question 3

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It specifies the meaning of mathematical statements?

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### Question 4

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

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### 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?

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### Question 6

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It refers to statements that supports the arguments?

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### Question 7

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

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### 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?

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### Question 9

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

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### Question 10

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Objects that can be counted are called?

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