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# Discrete Structures 2

#### Showing 1-75 of 106 answers

A full binary tree with 2n+1 nodes contain
• n-1 leaf nodes
• n non-leaf nodes Correct
• n-1 non leaf nodes
• n leaf nodes
A node is _____________
• An elements Correct
• The tail
A queue is a FIFO list
• True Correct
• False
A train is an example of _____ data structure
• Queue
• Stack
• None of the choices
• Algorithm Data Type
• Abstract Dynamic Traversing
• Array Data Type
• Abstract Data Type Correct
An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space Determine the event that the sum of the numbers falling uppermost is greater than or equal to 7.
• {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)}
• {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
• {(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} Correct
Assume that you have an ordinary deck of 52 playing cards. How many possible 7-card poker hands are there that contain at least one face card (J, Q, K)?
• C(12,3) =C2=B7 C(40,4)
• C(4,1) =C2=B7 C(4,1) =C2=B7 C(4,1) =C2=B7 C(40,4)
• C(12,1) =C2=B7 C(40,6)
• C(52,7) - C(40,7) Correct
Consider the following finite automaton A over =CE=A3 = {a,b,c}:Which of the following statements about A is/are correct?
• =C9=9B =E2=88=88 L(A)
• bbaacbabcac =E2=88=88 L(A) Correct
• bacabca =E2=88=88 L(A)
• The automaton A is a Deterministic Finite Automaton (DFA)
Consider the statement "If the product of two integers is even, then their sum is also even." Which of the following assertions is correct?
• The statement is true and can be proven easily using either direct proof or proof by contradiction
• The statement is true and can be proven easily using either direct proof or proof by contraposition
• The statement is false as you can find a counterexample Correct
• The statement is true and can be proven easily using either direct proof
Consider the statement, =E2=80=9CIf n is divisible by 30 then n is divisible by 2 and by 3 and by 5.=E2=80=9D Which of the following statements is equivalent to this statement?
• If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30 Correct
• If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5
• If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30
• If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by 5
Data structure is defined as a specialized format for _______ and ______ data
• inserting, deleting
• processing, sorting
• organizing, storing Correct
• searching, processing
Describe the process of removing an element at the tail of a singly linked list
• Removing an element at the tail of the singly list is very fast
• Removing an element at the tail of the singly list is not easy Correct
• Element at the tail of the singly linked list cannot be removed or deleted
• None of the choices
How many edges does a tree with V vertices have?
• V - 1 Correct
• infinite
• V2
• V + 1
• V
How may isomorphic graphs are there for a graph with n number vertices?
• (n + 1)! number of vertices
• (2n - 1)! number of vertices
• (n - 1)! number of vertices
• n! number of vertices Correct
• choosing a suitable algorithm
• None of the choices
• choosing a data representation Correct
• choosing a suitable algorithm and data representation
In examining the algorithm of multiplying two numbers and displaying the output, what is the next step after declaring the 3 integers a,b,c
• define the values of a and b Correct
• compute the product of a and b
• check if the numbers are positive numbers
• check which of the two numbers is higher
It is impossible for a valid argument to have a true premise and
• a conditional conclusion
• a false conclusion Correct
• a true conclusion
• a negated conclusion
Let P be the statement "you can make n cents postage using 3-cent and 5-cent stamps." Suppose you want to use the Principle of Mathematical Induction to show that P is true for all n =E2=89=A5 8.You begin by proving P(8), which is true because 8 cents postage can be made with one 3-cent stamp and one 5-cent stamp.Which of the following will show that the implication P(k) -> P(k+1) in the inductive step is true for all k =E2=89=A5 8?
• Take all stamps that are used to make k cents postage, remove a 5-cent postage and replace with a 3-cent stamp
• Take all stamps that are used to make k cents postage and add a 3-cent stamp
• none of the given Correct
• Take all stamps that are used to make k cents postage and add a 5-cent stamp
• Take all stamps that are used to make k cents postage, remove three 3-cent postage and replace with two 5-cent stamp
Logic is a system based on __________.
• truth values
• statements
• truth tables
• propositions Correct
Suppose that P is the statement "n + 1 = n + 2". What is wrong with the following proof that the statement P is true for all non negative integers n?You assume that P(k) is true for some positive integer k, that is, that k+1 = k+2. Then you add 1 to both sides of this equation to obtain k+2 = k+3; therefore P(k+1) is true. By the principle of mathematical induction P is true for all non-negative integers n.
• The proof is incorrect because you cannot add one to both sides of the equation in the inductive step
• There is nothing wrong with this proof
• The proof is incorrect because there is no basis step Correct
• The proof is incorrect because the statement used in the inductive hypothesis is incorrect
Suppose you want to prove that every product of integers of the form k(k+1)(k+2) is divisible by 6. If you want to prove this by cases, which of the following is a set of cases you would use?
• the product ends in 3, the product ends in 6, the product ends in 9
• when k is divided by 3, the remainder is 0; when k is divided by 3, the remainder is 1; when k is divided by 3, the remainder is 2 Correct
• k = 3n, k =E2=89=A0 3n
• k is prime, k is not prime
Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all positive integers n. Which of these is the correct implication p(k) -> P(k+1) to be used in the inductive step?
• 1 + 2 + 22 + 23 + + 2k = 2k+1 - 1 -> 1 + 2 + 22 + 23 + 24 + + 2k + 2k+1 - 1
• 1 + 2 + 22 + 23 + + 2k = 2k+1 - 1 -> 1 + 2 + 22 + 23 + + 2k + 2k+1 = 2k+1 - 1 + 2k+1
• 2k -> 2k+1 - 1
• 1 + 2 + 22 + 23 + + 2k = 2k+1 - 1 -> 1 + 2 + 22 + 23 + + 2k + 2k+1 = 2k+2 - 1 Correct
Suppose you wish to prove this statement "If n is an integer, then n =E2=89=A4 n3." Which of the following is correct?
• The given statement is true and can be proven easily using a direct proof
• The given statement is true and can be proven easily using contradiction
• The given statement is false because a counterexample can be found Correct
• The given statement is true and can be proven easily using mathematical induction
The basic limitation of finite automata is that
• All of the mentioned
• It cannot  remember arbitrary large amount of information Correct
• It cannot process strings of length greater than 5
• It sometimes fails to recognize regular grammar
• It sometimes recognize grammar that are not regular
The first node of a linked list is referred to as _____________
• main node
• base pointer
• pointer
The method of accessing the element in a linked list is _______
• Traversal Correct
• By specifying the index element
• Random access
• Direct access
The number of cars entering a tunnel leading to an airport in a major city over a period of 200 peak hours was observed and the following data were obtained: Cars, xFrequency of Occurrence152040654515Find the empirical probability distribution for this experiment.
• Cars, x           Frequency of Occurrence                0075              0225              0325              02             01                  0075
• Cars, x           Frequency of Occurrence                0075              01              02              0325             0225                  0075      Correct
• Cars, x           Frequency of Occurrence                0077              0102              0198              0323             0225                  0075
• Cars, x           Frequency of Occurrence                0077              0098              0202              0323             0227                  0073
The results of a time study conducted by the production manager of Ace Novelty are shown in the accompanying table, where the number of space action-figures produced each quarter hour during an 8-hour workday has been tabulated. Find the empirical probability distribution associated with this experiment. Figures Produced (in dozens)Frequency of Occurrence304310326336348356362
• Figures        Frequency of Produced       Occurrence(in dozens)30             0062531             0187532             02533             0187534             0187535             036             0125
• Figures        Frequency of Produced       Occurrence(in dozens)30             0125131             032             0187633             0187434             0249935             0187536             00625
• Figures        Frequency of Produced       Occurrence(in dozens)30             0125131             0000132             0187433             0187434             02535             0187536             00625
• Figures        Frequency of Produced       Occurrence(in dozens)30             012531             032             0187533             0187534             02535             0187536             00625 Correct
The size need to be specific during declaration
• The statement applies to both array and linked list
• The statement describes a linked list
• The statement describes an array Correct
• The statement does not apply to array and linked list
This is a statement that is always false.
• tautology
• implication
• conjunction