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web.groovymark@gmail.com
- November 9, 2024
Question 41
What defines a complete Boolean expression?
a) It has no redundant elements
b) It includes all variables
c) It uses all possible operations
d) It cannot be simplified further
Correct Answer: d) It cannot be simplified further
Explanation: A complete Boolean expression is structured such that it cannot be further reduced or simplified without losing its original meaning or truth value.
Question 42
What is the purpose of an identity function?
a) It maps every element onto itself
b) It provides a constant output
c) It maps elements randomly
d) It transforms data
Correct Answer: a) It maps every element onto itself
Explanation: An identity function is defined as a function where each element in the set is mapped to itself, maintaining the original value.
Question 43
Which property characterizes a binary relation?
a) It must be symmetric
b) It consists only of ordered pairs
c) It must be reflexive
d) It must be transitive
Correct Answer: b) It consists only of ordered pairs
Explanation: A binary relation is defined as a set of ordered pairs, which establishes a relationship between elements of two sets.
Question 44
What does the notation ¬p∧q indicate?
a) Both p and q are true
b) p is false and q is true
c) Either p or q is true
d) p is true and q is false
Correct Answer: b) p is false and q is true
Explanation: The expression ¬p∧q indicates that p is false while q is true, thus combining the negation of p with q using the logical AND operator.
Question 45
Which of the following represents a logical equivalence?
a) Two propositions with different truth values
b) Two propositions that always have the same truth value
c) A proposition and its negation
d) A proposition that can only be true
Correct Answer: b) Two propositions that always have the same truth value
Explanation: Logical equivalence occurs when two propositions yield identical truth values in all possible scenarios, indicating that they convey the same logical information.
Question 46
What does a directed edge in a graph indicate?
a) It is a bidirectional connection
b) It indicates a relationship with a specific direction
c) It shows a loop
d) It connects two vertices without direction
Correct Answer: b) It indicates a relationship with a specific direction
Explanation: A directed edge represents a one-way relationship between two vertices in a graph, indicating the direction of the connection.
Question 47
What is the relationship between a proper subset and a subset?
a) A proper subset must be larger than the set
b) A proper subset must have more elements than the set
c) A proper subset can be equal to the set
d) A proper subset cannot be equal to the set
Correct Answer: d) A proper subset cannot be equal to the set
Explanation: A proper subset contains some but not all elements of the set and cannot be equal to the original set, which would classify it as an improper subset.
Question 48
What is the defining feature of a function that is not injective?
a) Every element of the domain maps to a unique element in the codomain
b) At least one element in the domain maps to multiple elements in the codomain
c) Every element in the codomain has a corresponding element in the domain
d) The function has no outputs
Correct Answer: b) At least one element in the domain maps to multiple elements in the codomain
Explanation: A function is not injective if there are distinct elements in the domain that map to the same element in the codomain, indicating a loss of uniqueness.
Question 49
In terms of logic, what does the phrase “if p, then q” express?
a) A conjunction
b) A disjunction
c) A conditional statement
d) A contradiction
Correct Answer: c) A conditional statement
Explanation: The phrase "if p, then q" signifies a conditional statement, where the truth of q is dependent on the truth of p.
Question 50
What is the implication of finding a counterexample in a proof?
a) It supports the claim
b) It disproves the statement
c) It proves the statement
d) It validates the hypothesis
Correct Answer: b) It disproves the statement
Explanation: A counterexample serves as evidence that a general statement or claim is false, thereby disproving the assertion being examined.
