Which of the following is the correct definition of a set?
A Set of equations
B Collection of elements
C List of elements
D Group of numbers
A set is defined as a well defined collection of distinct objects, which can be anything like numbers, letters, or any other kind of entities. The order and repetition of elements do not matter.
What does the union of two sets represent?
A All subsets
B Difference of sets
C Common elements
D All elements
The union of two sets includes all the elements from both sets, without duplication. It is denoted by “A ∪ B” and combines every element from set A and set B.
Which symbol represents the complement of a set?
A ⊆
B ∩
C ′
D ∪
The complement of a set A, denoted as A′, refers to all elements not in A. It includes everything outside of set A in the universal set.
Which of the following is true about a bijective function?
A One-to-one and onto
B None of the above
C Onto only
D One-to-one only
A bijective function is both one to one (injective) and onto (surjective), meaning each element of the domain is mapped to a unique element of the codomain, and every element in the codomain is covered.
What is the result of the Boolean expression: A OR (B AND C)?
A A AND (B OR C)
B A OR (B AND C)
C (A AND B) OR C
D A AND B AND C
The Boolean expression “A OR (B AND C)” evaluates to true if A is true or both B and C are true. This follows the precedence of AND over OR in Boolean operations.
Which of the following is used to represent a graph in a computer system?
A List
B Graph table
C Matrix
D Set
A graph can be represented using an adjacency matrix, where each element in the matrix indicates whether there is an edge between two vertices. This is particularly useful for dense graphs.
Which of the following best describes a directed acyclic graph (DAG)?
A Bipartite graph
B Cyclic graph
C Directed and acyclic
D Non-directional graph
A directed acyclic graph (DAG) is a graph that has directed edges and contains no cycles. It is often used in scheduling tasks, representing dependencies, and other scenarios where directionality is important.
What does the principle of mathematical induction allow us to do?
A Prove theorems in number theory
B Prove statements for large numbers
C Prove statements for all integers
D Prove geometric theorems
Mathematical induction is a proof technique used to prove statements or formulas for all integers. It involves proving a base case and then assuming the statement holds for an integer k to prove it for k+1.
Which of the following is an operation used in Boolean algebra?
A Conjunction
B Exponentiation
C Division
D Multiplication
In Boolean algebra, conjunction (AND) is one of the basic operations. It returns true when both operands are true. Other Boolean operations include disjunction (OR) and negation (NOT).
What is the sum of the two numbers in mod 5 arithmetic: 3 and 4?
A 8
B 2
C 7
D 6
In modular arithmetic with mod 5, 3 + 4 equals 7. However, since we are working mod 5, we take the remainder when 7 is divided by 5, which gives 2.
What is the smallest possible degree for a vertex in a graph?
A 2
B -1
C 1
D 0
The smallest degree of a vertex in a graph is 0. This occurs when the vertex is isolated and has no edges connected to it.
Which of the following is a valid subset of set {1, 2, 3}?
A {1, 2}
B {2, 4}
C {3, 4}
D {4, 5}
A subset is a set that contains only elements from the original set. Therefore, {1, 2} is a valid subset of {1, 2, 3}, as both elements are part of the original set.
In graph theory, what is the shortest path between two vertices called?
A Diameter
B Edge count
C Distance
D Path length
In graph theory, the shortest path between two vertices is called the distance between them. This is the minimum number of edges that must be traversed to reach one vertex from another.
What does a matrix represent in Discrete Mathematics?
A Logical relationships
B Graphical data
C Operations on sets
D System of equations
In Discrete Mathematics, a matrix is often used to represent a system of linear equations. Each row corresponds to an equation, and the columns represent the coefficients of the variables.
What is a relation in mathematics?
A A connection between elements of two sets
B A set of equations
C A function from one set to another
D A group of numbers
A relation in mathematics is a set of ordered pairs, where the first element is from one set and the second element is from another set. It describes a relationship between elements of two sets.