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Cis1910
| Question | Answer |
|---|---|
| the initial term is also know as the ______ | basis |
| What is induction? | reasoning from the particular to the general; what’s true for particulars should be true for all other instances a proof technique for verifying conjectures based on positive integers useful for proving recurrences and verifying recursive algorithms |
| What is the process of verifying propositions by induction | 1. Basis step- plug the first value into the function and prove it holds 2. Inductive step, plug k in, does it still hold? state the inductive hypothesis when n = k 3. consider n = k + 1, reduce it to a problem and simplify |
| When verifying propositions by induction, In the inductive step, the statement P (k) is called the______ the more general proof uses ____ instead of P(k) | inductive hypothesis, P(k+1) |
| which process does this summarize? If we show that P (no) is true and prove for all k ≥ no that assuming P (k) is true implies P (k + 1) is also true, then way may conclude P (n) is true for all n ≥ no | Process of proof by induction |
| what is the difference between strong induction vs normal induction | strong is P(k+1) normal is P(k) |
| What property is this, Every nonempty set of non-negative integers has a least element. | Well ordering Property |
| S = {1, {1}, {1, {1}}} what's the cardinality | 3 |
| let a function be Bijective what does this mean? | it is both surjective and injective |
| Two vertices u and v are said to be adjacent or neighbors if | There is an edge between them |
| An edge is also known as an _________ to u and v (the vertices) | incident |
| The _______ of a vertex v, denoted _____, is the number of edges incident with it (the number of v’s neighbors) | degree, deg (v) |
| A vertex with degree 0 is called | isolated |
| A vertex with degree 1 is called | pendant |
| how do you find the degree of a point on a graph | look and see how many connections it has |
| If (u, v) is an edge in a directed graph, then u is adjacent ___ v, and v is adjacent ____ u. | to, from |
| The _________ of a vertex v is the number of edges directed into v | in degree |
| The __________ of a vertex v is the number of edges directed out of v - with v as the initial vertex | out degree |
| The sum of in degrees is equal to the sum of ______ and the number of________ | out degrees, edges |
| The nth term of ceiling (root n) | non decreasing |
| The first two terms in the sequence are 1. The rest of the terms are the sum of the two preceding terms. | non decreasing |
| what is this 1,2,3,4,5,6 | increasing, non decreasing |
| 10, 7, 4, 1, -2 | decreasing, non increasing |
| 5, 5, 5, 1/2, 1/3 | non increasing |
| 0, 0, 0, 0, 1, 2, 3, 4 | non decreasing |
| 7, 7, 7, 7, 7, 7 | non increasing and non decreasing because its constant |
| Is every sequence that is increasing also non decreasing? | Yes |
| Is every non decreasing sequence also increasing? | No |
| What is a haplotype | is a unique DNA sequence that differs from other such DNA sequences at one or more nucleotide sites |
| What is Hamming distance | One way to calculate the distance between pairsof haplotypes, this method finds the num of differences |
| Hamming distance is one, whats another way to calculate distance | p-distance, this is hamming distance scaled by DNA sequence length. can alse be calculated based on generated multiple sequence allignments (MSA) using software likeMEGA |
| What are haplotype networks | Haplotype networks are a type of undirected graph depicting evolutionary relationships among sampled DNA sequences for taxa of interest such as species at-risk or invasive species |
| Circles represent haplotypes, where the size of _____________ reflects the number of DNA sequences contained within a given haplotype | vertices/ nodes |
| Tick/hash marks (–) along edges reflect the number of ____________________ separating two distinct haplotypes, but edge length is meaningless | Mutations/substitutions |
| What are 3 examples of haplotype networks | Minimun spanning haplotype Network/Tree (MST) TCS (Templeton Crandall Sing) Network Median Joining Network (MJN) |
| What are 3 types if existing software | TCS (Java software) pegas (R package) PopArt |
| two vertices are adjacent or neighbors if they share an________, this b;ank is said to be _______ to both verices | edge, incident |
| What is the Handshaking theorem | ifits an undirected graph then each edge gets counted twice when summing degrees |
| What is the bipartite theorumn | graph is bipartite if and only if it is possible to color the vertices with twocolors such that no two adjacent vertices have the same color. |
| a _______ in a simple graph G = (V, E) is a subset of E such that no two edges are incident with the same vertex | matching |
| A __________ is a matching with with the largest number of edges. | maximum matching |
| When is a subgraph induced | if it has all its edges from the orginal graph with the given vertices |
| What is the order of precedence | 1. NOT 2. AND 3. OR 4. IF–THEN 5. IFF |
| p→q p ∴ q | Modus Ponens also affirming the antecedent |
| p→q ¬q ∴ ¬p | Modus Tollens |
| p∨q ¬p ∴ q | Disjunctive Syllogism |
| p→q q→r ∴ p→r | Hypothetical Syllogism |
| (p→r)∧(q→s) p∨q ∴ r∨s | Constructive Dilemma |
| p→q q ∴ p (❌ invalid) | Affirming the Consequent, you cant determine p from q |
| The scope of the quantifier | whatever is inside the bracket, it immediately follows the quantifier |
| The number of rows in a truth table is 2^n , where n is the number of distinct truth values (T/F) | False n = the number of variables |
| The assertion "The correct answer to the previous question is false" is a proposition (T/F) | True |
| What is a proposition | It is a fact, it cannot be a question or a contradiction like this statement is false, it also cannot be a command like close the door. It must have a distinct truth value |
| A contrapositive keeps the same truth value(T/F) | True |
| if xy = x then x = 1 and y = 1 (T/F) | False x and y could be 0 |
| ) is both positive and negative (T/F) | False 0 is neither positive or negative |
| Explain Liars paradox | "This statement is false" it cannot be consistently labeled either true or false, it is a paradox because it has more than one truthe value. another example is "I am lying" |
| What is true about prime numbers | If a prime number p divides a product ab then p must divide at least one of a or b |
Created by:
jayne_