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