Answer each question in the space below. 1. Let A = {0,1} U... U{0,1}5 and let...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
2. A binary string is a finite sequence u-діаг . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings ai, aia2,... ,ai... an-1,ai... an are all prefixes of v. On the set X of all binary strings consider the relations Ri and R2 defined as follows: Ri-(w, v) w and v have the same length ) R2 = {(u, v) I w is a prefix...
Discrete Math Please Help parts a and b Let A = {0,1}, and consider A*, the set of all bitstrings. Let s,t E A*. Consider the relation R, where s Rt if and only if bitstring s is a prefix of bitstring t. For example, 00111 R 0011101 because all the bits in the first bitstring make up the first five bits in the second string: 0011101. Classify the following statement as true or false: The relation R is antisymmetric....
2. A binary string s a finite sequence u = ala2 . . . an, where each ai įs either 0 or 1. In this case n is the length of the string v. The strings ai,aia2,...,ai...an-1,aan are all prefixes of v. On the set X of all binary strings consider the relations Ri and R2 defined as follows R, = {(u, u) | w and u have the same length } {(w, u) | w is a prefix of...
2. (24 pts) True/False. Circle T or F. No explanation needed. (a) T F If Ris the relation whose digraph is below, then Ris reflexive. (b) T F For the relation from part (a), R is symmetric (C) T F The relation Son {a,B,y,g} whose matrix is 100.1 - 0 1 0 0 0 0 1 0 1001 is an equivalence relation. (d) T F The relation S from part (C) is a partial order. (e) T F Let the...
2. A binary string is a finite sequence v = a1a2 . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings a1, a1a2, . . . , a1 . . . an−1, a1 . . . an are all prefixes of v. On the set X of all binary strings consider the relations R1 and R2 defined as follows: R1 = {(w, v) | w...
Can you #2 and #3? 6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determine if it is an equivalence relation on A. If it is, describe the equivalence classes. If it is not determine which properties of an equivalence relation fail. (a) a Hb a and b are the same age in (in years). (b) a Gb a and b have grandparent in common. 2) Consider the relation S(x,y):x...
1. Let T be the matrix T=10 3 acting on the complex vector space V C3 (a) Recall how T defines the structure of a C-module on C3. (b) Let p(x71, and let 2Compute the element p(x) v of C3 (c) Give a set of generators and relations for C3 over Cz] with the above module structure. (d) Write down the relations matrix (e) Recall the definition of minimal polynomial of a matrix. (f) What is the minimal polynomial of...
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...
Please answer question 6 5. Let T2 be the digraph whose vertex set is {0,1,2}2 (i.e., n-tuples of ternary entries) and where uv is an arc iff u - v E 10,01 modulo 3. For instance, ifu 10 and v 12, then u-v 01 modulo 3 and so there is an arc uv. Determine the diameter and radius of this digraph 6, (553 students) Generalize #5 to T,., the digraph whose vertex set is [0,1,2)" and uv is an arc...