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web.groovymark@gmail.com
- November 9, 2024
Question 21
What is a proper subset of a set A?
a) A that contains all elements of A
b) A that has fewer elements than A
c) A that has more elements than A
d) A that is equal to A
Correct Answer: b) A that has fewer elements than A
Explanation: A proper subset of a set A contains some, but not all, elements of A and cannot be equal to A, distinguishing it from an improper subset.
Question 22
Which of the following describes the operation of selection in a relational database?
a) Removing duplicates from a set
b) Choosing n-tuples that satisfy specific conditions
c) Combining multiple tables
d) Modifying existing records
Correct Answer: b) Choosing n-tuples that satisfy specific conditions
Explanation: The selection operation retrieves specific tuples from a relational database based on defined criteria, filtering data according to specified conditions.
Question 23
In a directed graph, what does the term “outdegree” refer to?
a) The number of edges directed towards a vertex
b) The total number of edges in the graph
c) The number of edges directed away from a vertex
d) The number of loops connected to a vertex
Correct Answer: c) The number of edges directed away from a vertex
Explanation: The outdegree of a vertex is defined as the count of directed edges that originate from that vertex, indicating its outgoing connections.
Question 24
What is the significance of an equivalence relation?
a) It must be anti-symmetric
b) It provides a way to group elements into equivalence classes
c) It has to be reflexive
d) It requires that all elements relate to each other
Correct Answer: b) It provides a way to group elements into equivalence classes
Explanation: An equivalence relation allows for the classification of elements into equivalence classes based on shared properties, facilitating the organization of related elements.
Question 25
What does the logical expression p∧¬q signify?
a) Both p is true and q is false
b) Either p or q is true
c) p is false or qqq is true
d) p is true regardless of q
Correct Answer: a) Both p is true and q is false
Explanation: The expression p∧¬q means that p must be true while q must be false, representing a conjunction of these conditions.
Question 26
What does it mean for two sets to be equivalent?
a) They must contain the same elements
b) They must have the same number of elements
c) They are equal in every aspect
d) They are disjoint
Correct Answer: b) They must have the same number of elements
Explanation: Two sets are considered equivalent if they contain the same cardinality, meaning they have the same number of elements, regardless of the specific elements they contain.
Question 27
Which operation represents the negation of a disjunction?
a) ¬(p∨q) = ¬p∨¬q
b) ¬(p∨q) = ¬p∧¬q
c) ¬(p∧q) = ¬p∧¬q
d) ¬(p∧q) = ¬p∨¬q
Correct Answer: b) ¬(p∨q) = ¬p∧¬q
Explanation: According to De Morgan's laws, the negation of a disjunction translates to the conjunction of the negations of its components.
Question 28
What is a valid argument in logical terms?
a) One where the conclusion is false
b) One where the premises are true and the conclusion is also true
c) One that contains contradictory premises
d) One that has no premises
Correct Answer: b) One where the premises are true and the conclusion is also true
Explanation: A valid argument is defined by the relationship that if all premises are true, the conclusion must also be true, establishing logical consistency.
Question 29
What is the primary purpose of a proof by contradiction?
a) To simplify a proof
b) To assume a statement is true and show it leads to a contradiction
c) To demonstrate the necessity of an argument
d) To provide examples
Correct Answer: b) To assume a statement is true and show it leads to a contradiction
Explanation: Proof by contradiction involves starting with the assumption that a statement is true and demonstrating that this leads to an inconsistency, thereby proving the original statement must be false.
Question 30
What is the primary function of the projection operation in a relational database?
a) To select specific tuples based on conditions
b) To add new records to a table
c) To retrieve only certain attributes from each tuple
d) To combine multiple tables
Correct Answer: c) To retrieve only certain attributes from each tuple
Explanation: The projection operation allows for the extraction of specific attributes from tuples in a relational database, disregarding other attributes.
Question 31
Which of the following statements is true regarding a symmetric difference?
a) It includes elements that are common to both sets
b) It includes elements that are unique to each set
c) It cannot contain any elements
d) It is equivalent to the intersection of the sets
Correct Answer: b) It includes elements that are unique to each set
Explanation: The symmetric difference comprises elements that are present in either set but not in both, effectively excluding shared elements.
Question 32
What does the notation ∀x P(x) express?
a) There exists an x such that P(x) is true
b) P(x) is true for at least one x
c) P(x) is true for all x in the domain
d) P(x) is false for all x
Correct Answer: c) P(x) is true for all x in the domain
Explanation: The notation ∀x P(x)) indicates that the predicate P(x) holds true for every element within the specified domain.
Question 33
In set notation, what does A∩B represent?
a) The symmetric difference between sets A and B
b) The union of sets A and B
c) The intersection of sets A and B
d) The difference between sets A and B
Correct Answer: c) The intersection of sets A and B
Explanation: The notation A∩B represents the intersection of sets A and B, including only those elements that are present in both sets.
Question 34
What is a universal quantifier used for in logic?
a) To specify that a statement is true for at least one instance
b) To express that a statement is true for all instances
c) To negate a statement
d) To provide a specific example
Correct Answer: b) To express that a statement is true for all instances
Explanation: The universal quantifier denotes that a particular predicate holds true for every element in the domain, establishing a general rule.
Question 35
Which of the following best describes a closed walk in graph theory?
a) It starts and ends at different vertices
b) It contains repeated vertices but not repeated edges
c) It starts and ends at the same vertex
d) It does not allow any vertices to repeat
Correct Answer: c) It starts and ends at the same vertex
Explanation: A closed walk begins and terminates at the same vertex, allowing for the possibility of repeating vertices along the way.
Question 36
What is an example of a contradiction?
a) A statement that is sometimes true
b) A statement that can be both true and false
c) A statement that is always true
d) A statement that is always false
Correct Answer: d) A statement that is always false
Explanation: A contradiction is defined as a statement that cannot be true under any circumstances, consistently yielding a false outcome.
Question 37
What does the term “disjoint sets” refer to?
a) Sets that contain some common elements
b) Sets that are identical
c) Sets that have no elements in common
d) Sets that include the empty set
Correct Answer: c) Sets that have no elements in common
Explanation: Disjoint sets are defined as sets that do not share any elements, meaning their intersection is empty.
Question 38
What is a key feature of a total order?
a) It is not reflexive
b) All elements are comparable
c) It cannot be symmetric
d) It does not require transitivity
Correct Answer: b) All elements are comparable
Explanation: A total order implies that any two elements within the set can be compared, establishing a specific arrangement among them.
Question 39
What is the purpose of the identity law in Boolean algebra?
a) To define an equivalence
b) To assert that an element remains unchanged when combined with the identity element
c) To demonstrate contradictions
d) To create new logical expressions
Correct Answer: b) To assert that an element remains unchanged when combined with the identity element
Explanation: The identity law states that adding zero to a variable or multiplying it by one yields the original variable, demonstrating that the identity elements do not alter values.
Question 40
What does it mean for a relation to be anti-symmetric?
a) If xRy and yRx, then x must equal y
b) No elements are related
c) Every element relates to itself
d) If xRy then yRx must also hold
Correct Answer: a) If xRy and yRx, then x must equal y
Explanation: A relation is anti-symmetric if the presence of both xRy and yRx implies that x and y must be identical, establishing a strong condition on relationships.
