MATHEMATICS IN THE MODERN WORLD (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. FOLLOW THE INSTRUCTIONS CAREFULLY NO LONG EXPLANATION NEEDED. CHOOSE THE CORRECT ANSWER) Question 7The Hamming distance, d(x, y), of any two binary strings x and y satisfy each of the following properties EXCEPTd(x, y) = d (y,x)Od(x, y) = 0 if and only if x = y.Od(x, y) ≥d(x,z) + d(z,y)Ⓒd(x, y) ≥ 0

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Question 7 The Hamming distance, d(x, y), of any two binary strings x and y satisfy each of the following properties EXCEPT d(x, y) = d (y,x) Od(x, y) = 0 if and only if x = y. Od(x, y) ≥ d(x,z) + d(z,y) Ⓒd(x, y) ≥ 0

Question 7 The Hamming distance, d(x, y), of any two binary strings x and y satisfy each of the following properties EXCEPT d(x, y) = d (y,x) Od(x, y) = 0 if and only if x = y. Od(x, y) ≥ d(x,z) + d(z,y) Ⓒd(x, y) ≥ 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 18E

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34. Let be the set of eight elements with identity element and noncommutative multiplication given by for all in (The circular order of multiplication is indicated by the diagram in Figure .) Given that is a group of order , write out the multiplication table for . This group is known as the quaternion group. (Sec. Sec. Sec. Sec. Sec. Sec. Sec. ) Sec. 22. Find the center for each of the following groups . a. in Exercise 34 of section 3.1. 32. Find the centralizer for each element in each of the following groups. a. The quaternion group in Exercise 34 of section 3.1 Sec. 2. Let be the quaternion group. List all cyclic subgroups of . Sec. 11. The following set of matrices , , , , , , forms a group with respect to matrix multiplication. Find an isomorphism from to the quaternion group. Sec. 8. Let be the quaternion group of units . Sec. 23. Find all subgroups of the quaternion group. Sec. 40. Find the commutator subgroup of each of the following groups. a. The quaternion group . Sec. 3. The quaternion group ; . 11. Find all homomorphic images of the quaternion group. 16. Repeat Exercise with the quaternion group , the Klein four group , and defined by
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رجل QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ 2) (x1+x₂)² X₁ + X₂ X₁-X2 what dist of 2X² 3) X² + X²
the book is "First Course on Fuzzy Theory and Applications"
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There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (j) {(0, 1), (1, 1)} (m) {(0,0), (0, 1), (1, 1)} (b) {(0, 0)} (e) {(1, 1)} (h) {(0, 0), (1, 1)} (k) {(1, 0), (1, 1)} (c) {(0, 1)} (f) {(0, 0), (0, 1)} (i) {(0, 1), (1,0)} (1) {(0,0), (0, 1), (1, 0)} (0) {(0, 1), (1, 0), (1, 1)} (n) {(0,0), (1,0), (1, 1)} (p) {(0, 0), (0, 1), (1, 0), (1, 1)} For a-f use the letters for each relation above. a. List the reflexive relations on the set {0, 1}. b. List the irreflexive relations on the set {0, 1}. c. List the symmetric relations on the set {0, 1}. d. List the transitive relations on the set {0, 1}. e. List the antisymmetric relations on the set {0, 1}. f. List the asymmetric relations on the set {0, 1}.
4) Consider the equivalence claim: (Vx E R)(3! y E R)P(x,y) = (3! y E R)(Vx E R)P(x,y). (4.1) What is the domain of the predicate P(x, y)? (4.2) Give an example of a predicate P(x, y) for which the above claim is true. (4.3) Give an example of a predicate P(x, y) for which the above claim is false.