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The study of mathematical structures that can be considered "discrete" rather than "continuous" and include integers, graphs, and statements
What is the 4th and 8th element of aNo= n^(2) ?
Find |A ∩ B| when A = {1, 3, 5, 7, 9} and B {2, 4, 6, 8, 10}
Determine the number of elements in A U B.
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Consider the function f : N → N given by f (0) 0 and f (n + 1) f No + 2n + 1. Find f (6).
How many people takes coffee but not tea and wine?
Let A = {3, 4, 5}. Find the cardinality of P(A).
A connected graph with no cycles.
A graph T is a tree if and only if between every pair of distinct vertices of T there is a unique path.
A graph is complete if there is a path from any vertex to any other vertex.
The sum of the geometric progression is called geometric series
A sequence of vertices such that every vertex in the sequence is adjacent to the vertices before and after it in the sequence
Tracing all edges on a figure without picking up your pencil or repeating and starting and stopping at different spots
What is the line covering number of for the following graph?
De Morgan's law is used in finding the equivalence of a logic expression using other logical functions.
The cardinality of {3, 5, 7, 9, 5} is 5.
surjective and injecive are opposites of each other.
If two vertices are adjacent, then we say one of them is the parent of the other, which is called the _____ of the parent.
Does this graph have an Euler Path, Euler Circuit, both, or neither?
A _____ graph has no isolated vertices.
A path which visits every vertex exactly once
Circuits start and stop at _______________
A set of statements, one of which is called the conclusion and the rest of which are called premises.
The geometric sequences uses common _____ in finding the succeeding terms.
Defined as the product of all the whole numbers from 1 to n.
A function which renames the vertices.
The given graph is planar.
Two edges are adjacent if they share a vertex.
The child of a child of a vertex is called
_____ is the simplest style of proof.
The ________________________ states that if event A can occur in m ways, and event B can occur in n disjoint ways, then the event “A or B” can occur in m + n ways.
Which of the following is false?
Rule that states that every function can be described in four ways: algebraically (a formula), numerically (a table), graphically, or in words.
Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. If you will not give me a cow, then I will not give you magic beans.
A graph in which every pair of vertices is adjacent.
The _____ is a subset of the codomain. It is the set of all elements which are assigned to at least one element of the domain by the function. That is, the range is the set of all outputs.
The tree elements are called _____
Let ‘G’ be a connected planar graph with 20 vertices and the degree of each vertex is 3. Find the number of regions in the graph.
Find an element n of the domain such that f No = n.
An argument is said to be valid if the conclusion must be true whenever the premises are all true.
The number of edges incident to a vertex.
A sequence of vertices such that consecutive vertices (in the sequence) are adjacent (in the graph). A walk in which no edge is repeated is called a trail, and a trail in which no vertex is repeated (except possibly the first and last) is called a path
Euler paths must touch all edges.
What is the matching number for the following graph?
For all n in rational, 1/n ≠ n - 1
Which of the following the logic representation of proof by contrapositive?
What is the missing term? 3,9,__,81....
How many people like only one of the three?
Additive principle states that if given two sets A and B, we have |A × B| |A| · |B|.
Indicate which, if any, of the following graphs G = (V, E, φ), |V | = 5, is not connected.
Find the cardinality of R = {20,21,...,39, 40}
Solve for the value of n in :
Two graphs that are the same are said to be _______________
¬P ∨ Q is equivalent to :
In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices.
All graphs have Euler's Path
How many spanning trees are possible in the given figure?
If you travel to London by train, then the journey takes at least two hours.
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
A graph is an ordered pair G (V, E) consisting of a nonempty set V (called the vertices) and a set E (called the edges) of two-element subsets of V.
As soon as one vertex of a tree is designated as the _____, then every other vertex on the tree can be characterized by its position relative to the root.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A sequence of vertices such that consecutive vertices (in the sequence) are adjacent (in the graph). A walk in which no edge is repeated is called a trail, and a trail in which no vertex is repeated (except possibly the first and last) is called a path.
A Bipartite graph is a graph for which it is possible to divide the vertices into two disjoint sets such that there are no edges between any two vertices in the same set.
Deduction rule is an argument that is not always right.
A spanning tree that has the smallest possible combined weight.
A _____ is a _____ which starts and stops at the same vertex.
Find the cardinality of S = {1, {2,3,4},0} | S | = _____
It is an algorithm for traversing or searching tree or graph data structures.
A statement which is true on the basis of its logical form alone.
What is the type of progression?
What is the element n in the domain such as fNo = 1
Match the following properties of trees to its definition.
What is the sum from 1st to 5th element?
Does a rational r value for r2 =6 exist?
Find | R | when R = {2, 4, 6,..., 180}
How many simple non-isomorphic graphs are possible with 3 vertices?
What is the difference of persons who take wine and coffee to the persons who the persons who takes tea only?
These are lines or curves that connect vertices.
If n is a rational number, 1/n does not equal n-1.
A tree is the same as a forest.
The study of what makes an argument good or bad.
A simple graph has no loops nor multiple edges.
What is the minimum height height of a full binary tree?
Every connected graph has a spanning tree.
Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. If I will not give you magic beans, then you will not give me a cow.
The _____ of a a subset B of the codomain is the set f −1 (B) {x ∈ X : f (x) ∈ B}.
What is the 20th term?
How many edges would a complete graph have if it had 6 vertices?
Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. You will give me a cow and I will not give you magic beans.
It is a connected graph containing no cycles.
How many possible output will be produced in a proposition of three statements?
Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math. Translate "¬(P ν Q) → Q" into English.
Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. If I will give you magic beans, then you will give me a cow.
Fill in the blanks. A graph F is a _____ if and only if between any pair of vertices in F there is at most _____
It is a rule that assigns each input exactly one output
Which of the following statements is NOT TRUE?
How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
_____ is the same truth value under any assignment of truth values to their atomic parts.
Identify the propositional logic of the truth table given
A _____ is a function which is both an injection and surjection. In other words, if every element of the codomain is the image of exactly one element from the domain
The minimum number of colors required in a proper vertex coloring of the graph.
If the right angled triangle t, with sides of length a and b and hypotenuse of length c, has area equal to c2/4, what kind of triangle is this?
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a square, and the other is a triangle. Each shape is drawn in a single color. Suppose you believe me when I tell you that if the square is blue, then the triangle is green. What do you therefore know about the truth value of the following statement? The square is not blue or the triangle is green.
Arithmetic progression is the sum of the terms of the arithmetic series.
A sequence that involves a common difference in identifying the succeeding terms.
An undirected graph G which is connected and acyclic is called ____________.
Paths start and stop at the same vertex.
Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. If you will give me a cow, then I will not give you magic beans.
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a square, and the other is a triangle. Each shape is drawn in a single color. Suppose you believe me when I tell you that if the square is blue, then the triangle is green. What do you therefore know about the truth value of the following statement? If the triangle is green, then the square is blue.
Match the truth tables to its corresponding propositional logic
A graph for which it is possible to divide the vertices into two disjoint sets such that there are no edges between any two vertices in the same set.
How many people takes tea and wine?
_____ is a function from a subset of the set of integers.
Indicate which, if any, of the following three graphs G = (V, E, φ), |V | = 5, is not isomorphic to any of the other two.
¬(P ∨ Q) is logically equal to which of the following expressions?
Proofs that is used when statements cannot be rephrased as implications.
When a connected graph can be drawn without any edges crossing, it is called ________________ .
IN combinations, the arrangement of the elements is in a specific order.
An argument form which is always valid.
A _____ graph has two distinct groups where no vertices in either group connecting to members of their own group
match the following formulas to its corresponding sequence
How many people like apples only?
The number of simple digraphs with |V | = 3 is
Which of the following is a possible range of the function?
Find f (1).
What type of progression this suggest?
A _____ connected graph with no cycles. (If we remove the requirement that the graph is connected, the graph is called a forest.) The vertices in a tree with degree 1 are called _____
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