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# CS202: Discrete Structures Certification Exam Answers

Discrete structures refer to mathematical structures that deal with countable, distinct, and separable entities. They are essential in computer science, mathematics, and related fields for modeling and solving problems. Some common topics within discrete structures include:

1. Sets and Relations: Sets are collections of distinct objects, and relations describe the connections or interactions between elements of sets.
2. Functions: Functions map elements from one set to another, often used to describe relationships between variables.
3. Graph Theory: Graphs consist of vertices (nodes) and edges (connections between nodes), and they are used to model relationships and networks.
4. Combinatorics: Combinatorics deals with counting, arranging, and selecting objects, often involving permutations, combinations, and binomial coefficients.
5. Boolean Algebra: Boolean algebra deals with logical operations on truth values (true or false), fundamental for digital circuits and logic gates.
6. Discrete Probability: Probability theory applied to situations where outcomes are countable and finite, such as in games, algorithms, and cryptography.
7. Number Theory: Number theory deals with properties and relationships of integers, often used in cryptography and computer science algorithms.

Understanding discrete structures is crucial in various areas of computer science, including algorithms, data structures, cryptography, and theoretical computer science. They provide a foundation for reasoning about discrete systems and solving complex problems efficiently.

## CS202: Discrete Structures Exam Quiz Answers

• X = {1, 3, 9, 7}; Y = {3, 1, 7}
• X = {1, 3, 9, 7}; Y = {3, 1, 5, 9}
• X = {1, 3, 9, 7}; Y = {3, 1, 7, 9}
• X = {1, 3, 9, 7}; Y = {1, 3, 9, 7, 11}
• Y is equal to X
• Y is a subset of X
• Y is a superset of X
• Y is equal to the null set
• W – X – Y = Z
• W ∪ X ∪ Y = Z
• W X Y = Z
• W ⊕ X ⊕ Y = Z
• A
• B
• A B
• The empty set
• Elements in set X depend on specific elements in set Y
• Elements in set X must be independent of elements in set Y
• Elements in set X must entirely overlap with elements in set Y
• Elements in set X must be completely different from elements in set Y
• 6
• 7
• 8
• 9
• It can only meaningfully be called “completely true”
• It can meaningfully be either “completely true” or “completely false”
• It is “partially true”, where “partially” refers to some degree of truth
• It is “partially false”, where “partially” refers to some degree of falsehood
• True
• False
• Cannot be determined
• This is not a logical proposition
• E4 = E1 ^ E2 ^ E3
• E4 = E1 v E2 v E3
• E4 ⇔ E1 ⇔ E2 ⇔ E3
• E4 = ᆨE1 ^ ᆨE2 ^ ᆨE3
• L = (P ^ F) ^ (S ^ (D ^ I))
• L = (P ^ F) ^ (S (D ^ I))
• L = (P ∨ F) ∨ (S ^ (D ∨ I))
• L = (P ∨ F) ∨ (S ∨ (D ∨ I))
• Mary has been enabled by Susan
• Mary has been enabled by Michael
• Mary has an implied role in Susan’s success
• Mary has nothing to do with Susan’s success
• Showing P (0)
• Showing P(n)
• Proving P(n-1) ⟹ P(n), n = 1, 2, 3, ….
• Proving P(n) ⟹ P (n + 1), n ∈ ℕ, the natural numbers
• 3/13
• 4/51
• 4/51
• 11/52
• 0
• 1/ (210)
• 1/10
• ½
• 1/6
• 1/3
• 1/2
• 6/2
• f(x) = 2x
• f(y) = (2y) – 1
• f(n) = f(n-1) + 1
• P (A ∪ B) = P(A) + P(B), where A and B are disjoint and P is the probability function
• 35,156
• -58,593
• -292,968
• 15 is not a member of the described sequence
• st = f(st-1)
• st = 0.002 * st-1
• st = 0.99998 * st-1
• st = st-1 – 0.99998
• Vertices and edges
• Vertices and nodes
• Directional notations
• Any graph that contains a circuit
• A graph with a path whose vertex list contains every vertex of the graph
• A graph that contains a circuit, touching each edge of the circuit exactly once
• A graph with a path whose vertex list contains each vertex of the graph exactly once
• Assessment State
• Initial State
• Operational State
• Shutdown State
• There are only two cycles
• There are only two subtrees
• Each vertex has one or more subtrees
• Each vertex has no more than two subtrees
• A system terminal is active. It remains active until logout. Upon successful login, the system is accessible until logout.
• A system terminal sits idle. It remains idle until login is attempted. Two failed login attempts are allowed. The third causes the terminal to become disabled. Reset by a system administrator is then required for the terminal to be re-enabled. Upon successful login, the system is accessible until logout.
• A system terminal sits idle. It remains idle until login is attempted. Two failed login attempts are allowed. The third causes the terminal to become disabled. Automatic reset then occurs after five minutes so that the terminal is re-enabled. Upon successful login, the system is accessible until logout.
• A system administrator enables an access terminal. The terminal then sits idle until login is attempted. Two failed login attempts are allowed. The third causes the terminal to become disabled. Reset by a system administrator is then required for the terminal to be re-enabled. Upon successful login, the system is accessible until logout.
• There can be multiple transitions specified for a given state data input or external action impacting the state; and for every data input or external action impacting a state, a transition specification must exist
• There can be only one transition specified for a given state data input or external action impacting the state; and for every data input or external action impacting a state, a transition specification must exist
• There can be multiple transitions specified for a given state data input or external action impacting the state; and for every data input or external action impacting a state, a transition specification need not exist since the system is assumed to remain in its present state until a transition event occurs
• There can be only one transition specified for a given state data input or external action impacting the state; and for every data input or external action impacting a state, a transition specification need not exist since the system is assumed to remain in its present state until a transition event occurs
• Finite
• Infinite
• A countable number of elements
• Not countable, but also not infinite
• Resolution
• Modus Tollens
• Modus Ponens
• Conjunctive specialization
• 10101010
• 1010010100
• 1001010010
• 100!90!
• If any fact is true then the conclusion is true
• The conclusion is true only when all facts are true
• A conclusion can be chosen at random regardless of the facts
• The conclusion is true when all facts are true or when no facts are true
• True
• False
• The result is logically incongruent
• Sheffer Stroke of (A ∪ B) and (C ∪ D)
• Set it equal to the probability of the just-prior causal event
• Divide the probabilities of the string of causal events into each other
• Add the probabilities of the individual outcomes that lead up to the event
• Multiply the probabilities of the individual outcomes that lead up to the event
• P(A∩B) = P(A) P(B)
• P(A∩B) = P(A) + P(B)
• P(A∩B) = P(A) / P(B)
• P(A∩B) = P(A) – P(B)
• An undirected graph can be traversed in exactly one direction
• A directed graph can be traversed in any direction from any node
• An undirected graph can be traversed in any direction from any node
• A directed graph has only one circuit with a traversal path is specified by directional notation
• S12
• S22
• S1 + S2
• S2 * S1
• Union of W, X, Y
• Intersection of W, X, Y
• W, X, Y are subtracted from each other
• W, X, Y are subtracted from the universal set
• They cannot be stated, and what will happen cannot be predicted
• They can be stated, and the probability of all possible outcomes lies along a uniform distribution
• They can be stated, but the actual outcome on any given trial cannot be predicted with any certainty
• They can be stated, and the actual outcome on any given trial can be predicted within a specified probability
• 25%
• 30%
• 50%
• 60%
• A fully-connected graph is necessary for traversal
• The design consumes appears sophisticated and is likely to be accepted
• Physical traversal requires multiple paths should a given path fail or be bottlenecked
• Application owners can charge for the additional computer time needed to determine the shortest path
• X = Ø
• Y ↔️ X
• Y ⟶ X
• X = ⇁Y
• Resolution
• Specialization
• Generalization
• Modus Ponens
• AA−b
• (A−b)!
• P (A, A−b)
• (A/A−b)
• E4 = E1 ^ E2 ^ E3
• E4 = E1 v E2 v E3
• E4 ⊕ E1 ⊕ E2 ⊕ E3
• E4 = ᆨE1 v ᆨE2 v ᆨE3
• ¬A ∨ ¬B ^ C ^ D
• ¬A ^ ¬B C D
• A ^ B ∨ ¬C ∨ ¬D
• ¬A ^ ¬B ∨ ¬C ∨ ¬D
• C is a subset of D
• D is a subset of C
• For some x in D, P(x)
• There exists an x in D
• a → z
• a ⇔ z
• a z
• a ⇏ z
• Analogy
• Deductive
• Inductive
• Reductive
• 20%
• 40%
• 50%
• 60%
• No; you must also know the value of Fk for k = 0
• No; you must also know the value of Fk for k = 1 and k = 2
• Yes; the recursive sequence resolves itself as it proceeds
• Yes; you know everything you need to perform the calculation
• n + K, n ≥ 0
• n + 1, n ≥ 0
• n – K, n ≥ 0
• n – k, n ≥ K
• P = E*G(D)
• Pt = Et*G(Dt)
• Pt+1 = Et-1*G(Dt)
• Pt+1 = Et-1*G(Dt-1)
• A tree has no circular paths
• A tree cannot be fully traversed
• A tree has only one subgraph that contains a cycle
• 1 + 1 = 0
• 1 + 1 = 1
• 1 + 1 = 2
• 1 + 1 = 10
• Conjunctive specialization
• Disjunctive specialization
• Elimination
• Resolution
• They have different base cases
• They have different inductive steps
• They require different levels of proof
• They have different inductive assumptions
• Uses far less memory than its explicit version
• Can be calculated once the values of (a, b, c…) are known
• Defines none of its input parameter values (a, b, …) in terms related to those same parameter values
• Defines some or all of its input parameter values (a, b, …) in terms related to those same parameter values
• A tree within a connected graph that connects all nodes of the graph
• A subgraph of a connected graph that is a tree connecting all nodes of the graph
• A subgraph of a connected graph that connects all nodes of the graph with a minimum number of edges
• A subgraph of a connected graph that is a tree connecting all nodes of the graph with a minimum number of edges
• Resolution
• Elimination
• Disjunctive specialization
• Conjunctive specialization
• 4
• 8
• ≥ 4
• ≥ 8
• Contains a circuit that touches every edge of the graph exactly once
• Contains one or more circuits that touching each edge of the circuit exactly once
• Contains a circuit that contains most edges of the graph, touching each only once
• Has no circuits, and the graph can be traversed by touching every vertex exactly once
• Vertices, edges, edges with or without direction
• Nodes, links, edges without direction, no cycles
• Nodes, links, edges with or without direction, no cycles
• Nodes, links, edges with direction, only one cyclic subtree
• A graph is a tree
• A tree is a graph
• A graph is directed
• A tree can have a loop

Select one:

• The valve is closed
• The valve is not closed
• The valve remains in its present state
• The valve will alternate between open and closed
• By deduction on n for both series
• By induction on n for the first series and induction on k for the second series
• By induction on n2 for the first series and induction on kn for the second series
• By induction on n for the first series and induction on both k and n for the second series
• P(A)/P(B)
• P(A∪B)/P(B)
• P(A∩B)/P(A)
• P(A∩B)/P(B)
• S1 and S2 are independent
• S1 and S2 are not independent
• S1 and S2 were generated using a weak seed
• S1 and S2 were generated using a strong seed
• The result when n=0
• The result when k=0
• The result when k<0
• The result when n=0 and k=0