-
web.groovymark@gmail.com
- November 9, 2024
Question 01
Which of the following is the correct representation of a negation in logic?
a) p∧q
b) ¬p
c) p∨q
d) p→q
Correct Answer: b) ¬p
Explanation: The negation of a statement p is represented as ¬p, which means "not p." This is the correct way to negate a logical statement.
Question 02
Which of the following logical connectives represents a disjunction?
a) p∧q
b) ¬p
c) p∨q
d) p→q
Correct Answer: c) p∨q
Explanation: A disjunction is represented by p∨q, which means "p or q." This is true if at least one of the statements is true.
Question 03
What is the truth value of the logical implication p→q when p is true and q is false?
a) True
b) False
c) It depends on the context
d) Undefined
Correct Answer: b) False
Explanation: A logical implication p→q is false only when p is true and q is false.
Question 04
In which of the following situations is a biconditional statement p↔q true?
a) When p and q have different truth values
b) When p and q are both true or both false
c) When p is true and q is false
d) When p is false and q is true
Correct Answer: b) When p and q are both true or both false
Explanation: A biconditional statement p↔q is true only when p and q have the same truth values.
Question 05
Which of the following describes the contrapositive of p→q?
a) q→p
b) ¬p→¬q
c) ¬q→¬p
d) p↔q
Correct Answer: c) ¬q→¬p
Explanation: The contrapositive of p→q is ¬q→¬p, which flips and negates both statements.
Question 06
According to De Morgan’s Law, what is the correct negation of ¬(p∨q)?
a) ¬p∧¬q
b) ¬p∨¬q
c) ¬p∧q
d) p∨¬q
Correct Answer: a) ¬p∧¬q
Explanation: De Morgan's Law states that the negation of p∨q is ¬p∧¬q.
Question 07
Which of the following is always true in a tautology?
a) The statement is true under all possible interpretations
b) The statement is false under all possible interpretations
c) The statement is true only when p is true
d) The statement is true only when q is false
Correct Answer: a) The statement is true under all possible interpretations
Explanation: A tautology is a statement that is always true, regardless of the truth values of its components.
Question 08
Which of the following describes a contradiction in logic?
a) A statement that is always true
b) A statement that is always false
c) A statement that is sometimes true and sometimes false
d) A statement whose truth value is unknown
Correct Answer: b) A statement that is always false
Explanation: A contradiction is a statement that is always false, regardless of the truth values of its components.
Question 09
What is the empty set?
a) A set containing one element
b) A set containing no elements
c) A set containing all possible elements
d) A set containing infinite elements
Correct Answer: b) A set containing no elements
Explanation: The empty set is defined as the set with no elements.
Question 10
What is the power set of a set A containing 3 elements?
a) A set containing 3 elements
b) A set containing 2 elements
c) A set containing 6 elements
d) A set containing 8 elements
Correct Answer: d) A set containing 8 elements
Explanation: The power set of a set with n elements contains 2n subsets. For a set with 3 elements, the power set contains 23=8 subsets.
Question 11
Which of the following represents the union of two sets A and B?
a) A∩B
b) A∪B
c) A−B
d) A×B
Correct Answer: b) A∪B
Explanation: The union A∪B represents the set of all elements that are in A, in B, or in both.
Question 12
Which of the following represents the intersection of two sets A and B?
a) A∩B
b) A∪B
c) A−B
d) A×B
Correct Answer: a) A∩B
Explanation: The intersection A∩B is the set of elements that are in both A and B.
Question 13
Which of the following represents the set difference of A and B?
a) A∪B
b) A−B
c) A∩B
d) A×B
Correct Answer: b) A−B
Explanation: The set difference A−B contains elements that are in A but not in B.
Question 14
What is the Cartesian product of two sets A and B?
a) The set of all elements in A and B
b) The set of all ordered pairs (a,b) where a∈A and b∈B
c) The set of elements common to A and B
d) The set of elements in A but not in B
Correct Answer: b) The set of all ordered pairs (a,b) where a∈A and b∈B
Explanation: The Cartesian product A×B is the set of all ordered pairs formed by taking elements from A and B.
Question 15
Which of the following is a property of a reflexive relation?
a) Every element in the set relates to some other element
b) Every element in the set relates to itself
c) No element in the set relates to itself
d) Every element in the set relates to every other element
Correct Answer: b) Every element in the set relates to itself
Explanation: A reflexive relation requires that every element in the set is related to itself.
Question 16
Which of the following best describes an antisymmetric relation?
a) If a is related to b, then b is also related to a
b) If a is related to b and b is related to a, then a=b
c) Every element in the set relates to itself
d) No element in the set relates to any other element
Correct Answer: b) If a is related to b and b is related to a, then a=b
Explanation: In an antisymmetric relation, if two elements relate to each other in both directions, they must be equal.
Question 17
Which of the following defines a symmetric relation?
a) If a is related to b, then b is also related to a
b) Every element in the set relates to itself
c) No element in the set relates to itself
d) If a is related to b, then a is greater than b
Correct Answer: a) If a is related to b, then b is also related to a
Explanation: A symmetric relation ensures that if one element is related to another, the second element is also related to the first.
Question 18
Which of the following is an example of a transitive relation?
a) If a is related to b and b is related to c, then a is related to c
b) Every element in the set relates to itself
c) No element in the set relates to any other element
d) If a is related to b, then b is also related to a
Correct Answer: a) If a is related to b and b is related to c, then a is related to c
Explanation: A transitive relation ensures that if an element relates to a second element, and the second element relates to a third, then the first element relates to the third.
Question 19
Which of the following is a characteristic of an equivalence relation?
a) Reflexive, symmetric, and transitive
b) Antisymmetric and transitive
c) Symmetric and antisymmetric
d) Reflexive and antisymmetric
Correct Answer: a) Reflexive, symmetric, and transitive
Explanation: An equivalence relation must be reflexive, symmetric, and transitive.
Question 20
Which of the following is an example of a directed graph?
a) A graph with edges that have no direction
b) A graph with edges that have a direction
c) A graph with no edges
d) A graph where all vertices have the same degree
Correct Answer: b) A graph with edges that have a direction
Explanation: In a directed graph, edges are associated with a direction from one vertex to another.
