In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer.
Let A be the “punctured plane,”; that is, A is the set of all points in the Cartesian plane except the origin (0,0). A relation R is defined on A as follows: Fro every
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Chapter 8 Solutions
Discrete Mathematics With Applications
- Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.arrow_forwardGive an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.arrow_forwardTrue or False Label each of the following statements as either true or false. 2. Every relation on a nonempty set is as mapping.arrow_forward
- 11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.arrow_forwardGiven a set A = {1, 2, 3, 4}. Define a relation R on A as: R = {(x, y) | x - y is even} List the ordered pairs of the relation R. Is the relation R reflexive, symmetric, and transitive? Justify your answers.arrow_forwardLet A = {1, 2, 3, 4, 6). Let Ri be a relation defined on A. a. Verify reflexive property on the relation R;= {(1, 1), (1, 2), (2, 2), (3, 3), (3, 4), (4, 4), (6, 6)}. b. Verify symmetric property on the relation R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 3), (4, 4)}. c Verify asymmetric property on the relation R3 = {(1, 2), (2, 4), (3, 4), (4, 6), (6, 6)}.arrow_forward
- 1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b,a)} on set A = {a,b,c,d}. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why. 2. Consider the relation R = {(a,b),(a, c), (c, c), (b, b), (c, b), (b,c)} on the set A = {a,b,c}. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why. 3. Consider the relation R = {(a, b),(a, c), (c, b), (b, c)} on the set A = {a,b,c}. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why.arrow_forwardWhich of the following relations is transitive? Define a relation R in the natural number. Select the correct response(s): O R= {(x, y) I x + 2y = 7} R = xsy OR= {(x, y) I x + y = 8} R = {(x, y) I x – y = 4}arrow_forwardLet A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5), (3,3),(4,2), (4,4)}. Justify whether relation R fulfill the property of: i) Reflexive. ii) Symmetric.(iii) Anti-symmetric.(iv) Transitive.arrow_forward
- Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where? = {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the following properties R has: reflexive, symmetric, anti-symmetric, transitive? Justify your answer in each case?c) Let ? = {?, ?, ?} and ? = {(?,?), (?,?), (?,?), (?,?), (?,?)}, find [?], [?] and [?] (that is the equivalent class of a, b, and c). Hence or otherwise find the set of equivalent class of ?, ? and ??real number.i. State the domain of each of the two functionsii. Determine whether or not f is a one -to- one functioniii. Find the inverse of the function farrow_forwardProvide me complete solution of question please thanks 1arrow_forwardLet R = {(1, 2), (2, 3), (2, 4)} be a relation on {1, 2, 3, 4}. a. Show that R is not transitive. b. Find the transitive closure of R.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,