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web.groovymark@gmail.com
- November 9, 2024
Question 41
What does the symbol A\B represent?
a) The union of A and B
b) The intersection of A and B
c) The elements in A that are not in B
d) The symmetric difference of A and B
Correct Answer: c) The elements in A that are not in B
Explanation: The notation A\B denotes the difference between sets A and B, indicating the elements that belong to A but not to B.
Question 42
In graph theory, what distinguishes a trail from a path?
a) A trail cannot repeat vertices, while a path can
b) A path cannot repeat vertices, while a trail can repeat vertices
c) Both can repeat edges
d) Both can repeat vertices and edges
Correct Answer: b) A path cannot repeat vertices, while a trail can repeat vertices
Explanation: A trail allows for the repetition of vertices but restricts the repetition of edges, whereas a path does not allow for any repetition of vertices.
Question 43
What is the logical operation represented by the symbol ∧?
a) OR
b) AND
c) NOT
d) XOR
Correct Answer: b) AND
Explanation: The symbol ∧ represents the logical AND operation, indicating that both operands must be true for the overall expression to be true.
Question 44
What does the term “predicate” refer to in logic?
a) A variable that is not quantified
b) A logical statement that has a truth value dependent on variables
c) A specific instance of a logical expression
d) A statement that is always true
Correct Answer: b) A logical statement that has a truth value dependent on variables
Explanation: A predicate is a statement that contains one or more variables and becomes a proposition when specific values are assigned to those variables.
Question 45
What is an example of a tautology in logical expressions?
a) p∧¬p
b) p∨¬p
c) p→¬p
d) ¬(p∨p)
Correct Answer: b) p∨¬p
Explanation: The expression p∨¬p is a tautology because it is always true, regardless of the truth value of p.
Question 46
What does the notation ∃x P(x) signify?
a) There exists an x such that P(x) is false
b) P(x) is true for every x
c) P(x) is true for at least one x
d) P(x) is false for all x
Correct Answer: c) P(x) is true for at least one x
Explanation: The notation ∃x P(x) indicates that there is at least one element in the domain for which the predicate P(x) is true.
Question 47
What is the implication of a function being surjective?
a) It maps distinct elements to the same element
b) Every element in the codomain has at least one pre-image in the domain
c) It is not a function
d) It maps one element to multiple outputs
Correct Answer: b) Every element in the codomain has at least one pre-image in the domain
Explanation: A surjective function ensures that all elements of the codomain are covered by the mapping from the domain, with at least one element from the domain corresponding to each element in the codomain.
Question 48
Which of the following laws states that combining a set with the universal set yields the universal set?
a) Complement Law
b) Domination Law
c) Identity Law
d) Absorption Law
Correct Answer: b) Domination Law
Explanation: The Domination Law asserts that the union of any set with the universal set will always yield the universal set itself, as it encompasses all possible elements.
Question 49
What does the expression A∪∅equal?
a) A
b) B
c) ∅
d) The universal set
Correct Answer: a) A
Explanation: The union of any set A with the empty set results in A itself, as the empty set contributes no elements to the union.
Question 50
What does the notation A⊊B signify?
a) A is a subset of B
b) A is a proper subset of B
c) A and B are equal
d) A is not a subset of B
Correct Answer: b) A is a proper subset of B
Explanation: The notation A⊊B indicates that A is a proper subset of B, meaning all elements of A are in B, but B contains at least one element not in A.
