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Category > Computer Science Posted 23 Aug 2017 My Price 6.00

Homework 5 1. Enumerate the elements of the following relations from the set A of positive integers less than or equal to 10

Answer the questions clearly and thoroughly please..

Homework 5 1. Enumerate the elements of the following relations from the set A of positive integers less
than or equal to 10 to the set B of positive integers less than or equal to 30. (20 points, 2
parts- 10 points each)
a. An element a of A is related to the element b of B if b = 3 × a
b. An element a of A is related to the element b of B if b = 2 × a – 1 2. Determine the inverse of the following relations: (20 points, 2 parts- 10 points each)
a. The > relation defined on the integers
b. The = relation defined on the integers 3. Let A = {0, 1, 2, 3}. Define a relation R on A as follows: (20 points)
R = {(0, 0), ((1, 1), (2, 2), (1, 2), (2, 1), (2, 3), (3, 2)}.
Draw a directed graph for this relation and identify which of the following properties
hold for this relation: Reflexive
Symmetric
Transitive
Antisymmetric Explain why it has a property or give a counterexample.
4. Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the relation ≤
defined on S as follows: ((x1, y1) ≤ (x2, y2) if x1 ≤ x2 and y1 ≤ y2. Draw the directed graph
of this relation. Show that it is a partial order. Explain why it is not a total order. (20
points)
5. Consider the set S defined in problem 4 and the following relation = defined on S as
follows: (x1, y1) = (x2, y2) if x1 + y1 = x2 + y2. Draw the directed graph of this relation.
Show that it is an equivalence relation. List its equivalence classes. (20 points)
Grading Rubric:
Question
Question 1 Meets
20 points
Innovative and correct method of
solution. Does not Meet
0 points
Solution not described, or not
correct. 1 Question 2 Question 3 Question 4 Question 5 Calculations and supporting
evidence are complete and correct
for the problem. Calculations and supporting
evidence are incorrect or not
present. Solution is neat, well-organized
and well-written.
20 points
Innovative and correct method of
solution. Solution is unorganized and
poorly written.
0 points
Solution not described, or not
correct. Calculations and supporting
evidence are complete and correct
for the problem. Calculations and supporting
evidence are incorrect or not
present. Solution is neat, well-organized
and well-written.
20 points
Innovative and correct method of
solution. Solution is unorganized and
poorly written.

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Status NEW Posted 23 Aug 2017 02:08 PM My Price 6.00

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