-
web.groovymark@gmail.com
- November 9, 2024
Question 41
What is the outcome of A∪AC?
a) A
b) The empty set
c) The universal set
d) B
Correct Answer: c) The universal set
Explanation: The union of any set A with its complement AC results in the universal set, as it includes all possible elements.
Question 42
What does it mean for a statement to be universally quantified?
a) It is true for at least one instance
b) It is false for all instances
c) It is true for every instance
d) It is dependent on the context
Correct Answer: c) It is true for every instance
Explanation: A universally quantified statement asserts that a particular property holds true for all elements within the specified domain.
Question 43
What is the effect of combining a set with itself in a union operation?
a) It removes duplicates
b) It creates a larger set
c) It results in the empty set
d) It has no effect, the result is the same set
Correct Answer: d) It has no effect, the result is the same set
Explanation: The union of a set with itself yields the original set, as all elements are retained without duplication.
Question 44
Which of the following best describes a closed walk in a directed graph?
a) It can repeat vertices but not edges
b) It starts and ends at different vertices
c) It starts and ends at the same vertex
d) It does not allow any repetitions
Correct Answer: c) It starts and ends at the same vertex
Explanation: A closed walk is defined by returning to the starting vertex after traversing through edges, regardless of whether vertices are repeated.
Question 45
What does a proof by contraposition involve?
a) Assuming the original statement is true
b) Proving the contrapositive of the statement
c) Finding a counterexample
d) Demonstrating the truth of a single case
Correct Answer: b) Proving the contrapositive of the statement
Explanation: Proof by contraposition involves proving that if the conclusion is false, then the premise must also be false, thus establishing the truth of the original statement.
Question 46
What does the term “quantifier” refer to in logic?
a) A variable that is not defined
b) An operation that changes a statement
c) A symbol that expresses the quantity of a variable
d) A rule for negation
Correct Answer: c) A symbol that expresses the quantity of a variable
Explanation: A quantifier is a logical symbol that specifies the quantity of instances for which a predicate holds true, such as "for all" or "there exists."
Question 47
What does the term “logical equivalence” indicate?
a) Two statements can both be false
b) Two statements yield the same truth value under all interpretations
c) Two statements are unrelated
d) Two statements must be different
Correct Answer: b) Two statements yield the same truth value under all interpretations
Explanation: Logical equivalence occurs when two statements produce identical truth values in every possible scenario, indicating that they convey the same logical meaning.
Question 48
What does it mean if a set is countably infinite?
a) It has a finite number of elements
b) It can be put into one-to-one correspondence with the natural numbers
c) It contains only irrational numbers
d) It is larger than any finite set
Correct Answer: b) It can be put into one-to-one correspondence with the natural numbers
Explanation: A countably infinite set can be matched with the natural numbers, allowing for the establishment of a clear ordering of its elements.
Question 49
What is the result of A∩B when A and B are disjoint sets?
a) A
b) B
c) The universal set
d) The empty set
Correct Answer: d) The empty set
Explanation: The intersection of disjoint sets A and B yields the empty set, as there are no elements shared between the two sets.
Question 50
What does a function being “non-injective” imply?
a) Each element in the domain maps to a unique element in the codomain
b) At least two elements in the domain map to the same element in the codomain
c) It is bijective
d) It cannot be a function
Correct Answer: b) At least two elements in the domain map to the same element in the codomain
Explanation: A non-injective function indicates that there is a loss of uniqueness in mapping, where different inputs result in the same output.
