![4. [3 marks] Let R be a relation on a set A. Let A {1,2, 3, X, Y} and R = {(1, 1), (1,3), (2,1), (3, 1), (1, X), (X, Y)} (a)](http://img.homeworklib.com/questions/b15a0ec0-4e76-11eb-8c97-0be097187e71.png?x-oss-process=image/resize,w_560)
Homework Answers
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A,...
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
10. Represent the following relation R on the set (. t,s t) as a digraph and...
10. Represent the following relation R on the set (. t,s t) as a digraph and as a acro-ooe ati eachi b) Circle the properties of R antisymmetric itive 2 peins) reflexive symmetric 떼 1 find the symmetric and transitive closures ofS (4 pirtepi 1 c)If Ms-10 Transitive Closure Symmetric Closure_-
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by...
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
Let R be the relation defined on Z (integers): a R b iff a + b...
Let R be the relation defined on Z (integers): a R b iff a + b is even. R is an equivalence relation since R is: Group of answer choices Reflexive, Symmetric and Transitive Symmetric and Reflexive or Transitive Reflexive or Transitive Symmetric and Transitive None of the above
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff...
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...
4. Give the directed graph of a relation on the set ( x,y,z that is a)...
4. Give the directed graph of a relation on the set ( x,y,z that is a) not reflexive, not symmetric, but transitive b) irreflexive, symmetric, and transitive c) neither reflexive, irreflexive, symmetric, antisymmetric, nor transitive d) a poset but not a total order e) a poset and a total order
Let R be the relation defined on Z (integers): a R b iff a + b...
Let R be the relation defined on Z (integers): a R b iff a + b is even. Suppose that 'even' is replaced by 'odd' . Which of the properties reflexive, symmetric and transitive does R possess? Group of answer choices Reflexive, Symmetric and Transitive Symmetric Symmetric and Reflexive Symmetric and Transitive None of the above
8) Let R be a relation on the set A = {a, b, c} defined by...
8) Let R be a relation on the set A = {a, b, c} defined by R= {(a, a),(a, b), (a, c), (b, a), (b, b)}. (3 points)_a) Find Mr, the zero-one matrix representing R (with the elements of the set listed in alphabetical order). (2 points)_b) Is R reflexive? If not, give a counterexample. (2 points)_c) Find the symmetric closure of R. (3 points)_d) Find MR O MR.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f is 0(g)" on F is: (a) (4pt) Write down the definition for "f is O(g)". (b) (4pt) Prove that the...
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f is 0(g)" on F is: (a) (4pt) Write down the definition for "f is O(g)". (b) (4pt) Prove that the relation is reflexive (c) (6pt) Prove that the relation is not symmetric. (d) (6pt) Prove that the relation is transitive.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...
(4) (a) Give an example of a relation (different to those in question 1) which is...
(4) (a) Give an example of a relation (different to those in question 1) which is symmetric and transitive but not reflexive. (b) Identify the problem with the following proof: Let R be a relation on a set S, and suppose that R is symmetric and transitive. Since the relation is symmetric, we know that a bb~a, and then it follows from transitivity that a ~b and b ~ a → a ~ a. Therefore any symmetric and transitive relation...
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
10. Represent the following relation R on the set (. t,s t) as a digraph and as a acro-ooe ati eachi b) Circle the properties of R antisymmetric itive 2 peins) reflexive symmetric 떼 1 find the symmetric and transitive closures ofS (4 pirtepi 1 c)If Ms-10 Transitive Closure Symmetric Closure_-
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...
4. Give the directed graph of a relation on the set ( x,y,z that is a) not reflexive, not symmetric, but transitive b) irreflexive, symmetric, and transitive c) neither reflexive, irreflexive, symmetric, antisymmetric, nor transitive d) a poset but not a total order e) a poset and a total order
8) Let R be a relation on the set A = {a, b, c} defined by R= {(a, a),(a, b), (a, c), (b, a), (b, b)}. (3 points)_a) Find Mr, the zero-one matrix representing R (with the elements of the set listed in alphabetical order). (2 points)_b) Is R reflexive? If not, give a counterexample. (2 points)_c) Find the symmetric closure of R. (3 points)_d) Find MR O MR.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f is 0(g)" on F is: (a) (4pt) Write down the definition for "f is O(g)". (b) (4pt) Prove that the relation is reflexive (c) (6pt) Prove that the relation is not symmetric. (d) (6pt) Prove that the relation is transitive.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...
(4) (a) Give an example of a relation (different to those in question 1) which is symmetric and transitive but not reflexive. (b) Identify the problem with the following proof: Let R be a relation on a set S, and suppose that R is symmetric and transitive. Since the relation is symmetric, we know that a bb~a, and then it follows from transitivity that a ~b and b ~ a → a ~ a. Therefore any symmetric and transitive relation...
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