DS102: Propositional Logic Quiz

A proposition is a declarative sentence that can be either true or false, but not both.

Which of the following is NOT a proposition?

What is the area of logic that deals with propositions called?

A truth table is a tabular format that shows the truth value of a compound proposition for all possible combinations of its constituent propositions.

Which logical connective represents the negation of a proposition?

The truth value of the conjunction p ∧ q is true only when both p and q are true.

The truth value of the disjunction p ∨ q is true only when either p or q is true.

In the implication p → q, p is called the hypothesis and q is called the conclusion.

What is the name of the principle that states that 'a false statement implies anything'?

The truth value of the biconditional p ↔ q is true when p and q have different truth values.

A set is a collection of objects that can be anything conceivable, including other sets.

Match the following set notations with their descriptions:

A well-defined set ensures that it's always clear whether an object belongs to the set or not.

Two sets A and B are equal if and only if they have the same number of elements and the same exact elements.

What is the symbol used to represent the empty set?

What does the intersection of sets A and B, denoted as A∩B, represent?

What does the union of sets A and B, denoted as A∪B, represent?

What does the difference of sets A and B, denoted as A-B, represent?

The Cartesian product of sets A and B, denoted as A x B, is a set of all ordered pairs, where the first element comes from set A and the second element comes from set B.

A subset of a set U is a set that contains all the elements present in U.

Which of the following methods can be used to define a set?

The roster method describes a set by explicitly listing all its elements within curly braces.

The rule method uses a descriptive phrase to define a set based on the properties of its elements.

The statement form provides a well-defined description of the elements of a set, often enclosed in curly braces, using a clear and unambiguous statement.

A universal set is a set that contains all elements of all the related sets, without any repetition.

The symbols '⊆' and '⊂' are used to denote a subset and a proper subset, respectively.

Venn diagrams are pictorial representations of sets using closed figures, like circles or ovals, often enclosed in a rectangle representing the universal set.

Which of the following set operations is represented by the shaded region in a Venn diagram when two overlapping circles represent sets A and B?

Disjoint sets have no elements in common, and their intersection is an empty set.

The difference of sets A-B represents the set of elements that belong to A but not to B, visualized in a Venn diagram as the shaded region outside B and inside A.

The complement of a set A, denoted as A', within the universal set U, represents all elements of U that are not in A.

A function is a type of relation where every input is associated with exactly one output.

Number theory focuses on the study of natural numbers, particularly their divisibility properties.

An algorithm is a finite set of instructions that, when followed, accomplishes a specific task, typically independent of any specific programming language.

The time complexity of an algorithm measures the memory space required to execute an algorithm, while the space complexity measures the time taken to execute an algorithm.

The worst-case analysis of an algorithm determines the maximum number of steps an algorithm takes for any possible input of a given size.

A scheduling algorithm is a technique to organize and manage work and workloads on a CPU.

A Gantt chart is a graphical representation of a scheduling algorithm, portraying the timeline of tasks and their execution sequence.

Which scheduling algorithm is known for its simplicity and often used in situations like banks or shops?

Shortest Job First (SJF) scheduling aims to minimize the average waiting time for a set of processes by prioritizing the execution of the shortest jobs first.

Priority scheduling prioritizes the execution of tasks based on their assigned priority level, ensuring that high-priority tasks are completed first.

The Round Robin algorithm distributes a fixed amount of time, called a time quantum, to each process in a circular queue, ensuring fair CPU allocation and preventing any process from monopolizing the CPU.

Graph theory is a branch of mathematics concerned with networks of points connected by lines, often used to represent and analyze relationships between objects and their connections.

A multigraph is a type of graph that allows for multiple edges between any two vertices and loops (edges connecting a vertex to itself).

A planar graph is a graph that can be drawn in a plane without any edges crossing, except at a shared vertex.

A bipartite graph is a type of graph where the vertex set can be partitioned into two sets, and edges only connect vertices from opposite sets.

The Dudeney puzzle is a classic recreational problem in graph theory that challenges the construction of a system to connect three houses to three utilities without any pipes intersecting.

A vertex in a graph is a point that represents an object, and an edge connects two vertices, representing a relationship or connection between those objects.

A complete graph is a graph where every pair of vertices is connected by exactly one edge.

A connected graph is a graph where we can travel from any vertex to any other vertex by following a series of edges or paths.

A regular graph is a graph where every vertex has the same degree.

An acyclic graph is a graph that contains at least one cycle.

A bipartite graph is a graph where the vertex set can be partitioned into two sets so that each edge connects a vertex from one set to a vertex in the other set.

A star graph is a complete bipartite graph where n - 1 vertices have degree 1, connected to a single central vertex with degree n - 1.

A weighted graph is a graph where the edges are labeled with numbers, representing weights or costs associated with the connections.

The length of a path in a weighted graph is calculated by summing the weights of all edges in the path.

A measure of central tendency, like the mean, median, and mode, provides a single value that represents a typical or central point in a dataset.

The mean is calculated by summing all values in a dataset and dividing by the total number of values.

The median is the middle value in a dataset after sorting the values in either ascending or descending order.

The mode is the value that occurs most frequently in a dataset.

A frequency distribution summarizes a dataset by showing distinct values (categories) and the number of occurrences of each value (frequencies).

Measures of dispersion, such as the range, standard deviation, and variance, describe the spread or variability of data points around the central tendency.

The range is the most common measure of dispersion and is calculated by subtracting the minimum value from the maximum value in a dataset, which provides a measure of variability.

The standard deviation is calculated by taking the square root of the variance, indicating the average distance of data points from the mean, providing a more meaningful value than just the variance.

Which of the following is NOT a common type of measure of dispersion?