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