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web.groovymark@gmail.com
- November 8, 2024
Question 21
What is the union of sets A and B?
a) A ∩ B
b) A + B
c) A * B
d) A – B
Correct Answer: b) A + B
Explanation: The union of sets A and B, represented as A∪B, includes all elements that are in either A, B, or both.
Question 22
What does the difference between sets A and B denote?
a) Elements in A that are not in B
b) Elements common to both sets
c) All elements in either set
d) Elements in B that are not in A
Correct Answer: a) Elements in A that are not in B
Explanation: The difference A−B signifies the set of elements that are in A but not in B.
Question 23
How is the symmetric difference between sets A and B represented?
a) A ∩ B
b) A ∪ B
c) A Δ B
d) A – B
Correct Answer: c) A Δ B
Explanation: The symmetric difference, denoted AΔB, consists of elements that are in either A or B but not in their intersection.
Question 24
What is the complement of set A denoted as?
a) A’
b) A^C
c) A^c
d) A with a line over it
Correct Answer: d) A with a line over it
Explanation: The complement of set A, which includes all elements in the universal set that are not in A, is often denoted by à or a line over A.
Question 25
Which of the following laws states that rearranging the operator within a single union or intersection will not change its truth value?
a) Associative Laws
b) Commutative Laws
c) Absorption Laws
d) Distributive Laws
Correct Answer: b) Commutative Laws
Explanation: The Commutative Laws state that the order of elements does not affect the outcome of the union or intersection operations.
Question 26
What does De Morgan’s law state about the distribution of the complement operation?
a) It applies only to unions
b) It does not apply to intersections
c) The complement of a union is the intersection of the complements
d) The complement of an intersection is the union of the complements
Correct Answer: c) The complement of a union is the intersection of the complements
Explanation: De Morgan's laws indicate that the complement of a union of sets is equivalent to the intersection of their complements and vice versa.
Question 27
What does a directed graph consist of?
a) Only edges
b) Only vertices
c) Vertices and edges
d) None of the above
Correct Answer: c) Vertices and edges
Explanation: A directed graph, or digraph, is composed of two sets: vertices (points) and directed edges (lines connecting the points with a direction).
Question 28
What is the indegree of a vertex?
a) Number of edges pointing out of it
b) Number of edges pointing into it
c) Total number of vertices
d) Number of loops connected
Correct Answer: b) Number of edges pointing into it
Explanation: The indegree of a vertex refers to the count of directed edges that are directed towards that vertex.
Question 29
How is an open walk defined in graph theory?
a) It starts and ends at the same vertex
b) It has no restrictions on vertices
c) It starts and ends at different vertices
d) It cannot repeat any vertices
Correct Answer: c) It starts and ends at different vertices
Explanation: An open walk is characterized by having the first and last vertices be different, meaning it does not return to the starting vertex.
Question 30
What is a path in graph theory?
a) A walk that does not repeat any edges
b) A closed walk
c) A walk that does not repeat any vertices
d) An open walk with loops
Correct Answer: c) A walk that does not repeat any vertices
Explanation: A path is defined as a trail where no vertex is repeated, making it a unique sequence of vertices.
Question 31
Which operation takes a subset of attributes and deletes all other attributes in each of the n-tuples?
a) Selection operation
b) Projection operation
c) Join operation
d) Union operation
Correct Answer: b) Projection operation
Explanation: The projection operation in relational databases allows for selecting certain attributes from each n-tuple while disregarding the others.
Question 32
What defines a reflexive relation?
a) Every element relates to at least one other element
b) All elements in the set self-loop
c) No elements are related to themselves
d) Each pair of related elements has arrows pointing in both directions
Correct Answer: b) All elements in the set self-loop
Explanation: A relation is reflexive if every element in the set has a self-loop, meaning xRxxRxxRx holds true for all xxx in the set.
Question 33
What does it mean for a relation to be anti-symmetric?
a) Every element relates to itself
b) No pairs of distinct elements have both xRy and yRx
c) All elements are unrelated
d) Every element can only relate to itself
Correct Answer: b) No pairs of distinct elements have both xRy and yRx
Explanation: A relation is anti-symmetric if, for distinct elements x and y, xRy and yRx cannot both be true unless x is equal to y.
Question 34
Which statement is true regarding a bijective function?
a) It is both injective and surjective
b) It has no unique mappings
c) It can only map from X to Y
d) It has more elements in the target than the domain
Correct Answer: a) It is both injective and surjective
Explanation: A bijective function is defined as a function that is both injective (one-to-one) and surjective (onto), meaning every element in the domain maps uniquely to an element in the codomain.
Question 35
What is the Cartesian product of sets A and B?
a) The union of A and B
b) The intersection of A and B
c) A set of all ordered pairs from A and B
d) A set of elements common to both A and B
Correct Answer: c) A set of all ordered pairs from A and B
Explanation: The Cartesian product A×B is the set of all ordered pairs (a,b) where aaa is an element of A and b is an element of B.
Question 36
What does the term “pairwise disjoint” refer to?
a) All sets in the sequence share at least one common element
b) No two sets in the sequence share any elements
c) All sets have the same number of elements
d) Each set is a subset of the others
Correct Answer: b) No two sets in the sequence share any elements
Explanation: Pairwise disjoint sets are defined such that for every pair of distinct sets in the sequence, there are no elements in common.
Question 37
Which of the following is not a characteristic of a total order?
a) Reflexive
b) Symmetric
c) Transitive
d) Anti-symmetric
Correct Answer: b) Symmetric
Explanation: A total order requires the relation to be reflexive, transitive, and anti-symmetric, but it does not require symmetry, as total orders are strict.
Question 38
What is the key aspect of a relation being equivalence?
a) It must be anti-symmetric
b) It must be reflexive, symmetric, and transitive
c) It must include loops
d) It must be anti-reflexive
Correct Answer: b) It must be reflexive, symmetric, and transitive
Explanation: An equivalence relation satisfies the properties of being reflexive, symmetric, and transitive, allowing elements to be grouped into equivalence classes.
Question 39
In database terminology, what is an attribute?
a) A unique identifier
b) The data type stored in each entry of a table
c) A collection of records
d) A type of relationship between tables
Correct Answer: b) The data type stored in each entry of a table
Explanation: An attribute refers to the specific type of data that is stored in each column of a table, representing a characteristic of the data.
Question 40
What does the selection operation do in a relational database?
a) Deletes records from a table
b) Chooses n-tuples that meet specific conditions
c) Adds new records to a table
d) Modifies existing records
Correct Answer: b) Chooses n-tuples that meet specific conditions
Explanation: The selection operation is used to retrieve tuples from a relational database that satisfy given criteria or conditions on their attributes.
