(a) Let A = {a, b, c, d} and let R = (b, a), (c, c)}. (b) Let A = {1, 2, 3, 4, 5, 6, 7, 8} and let x R y whenever y is divisible by x. (c) Let A = {1, 2, 3, 4, 5, 6, 7, 8} and let x R y whenever x and y share no common factor other than 1. {(a. b), (b, d), (a, d). (d, a), (d, b), %3D 2. Determine which of the relations given in Exercise I are reflexive, which are symmetric, which are transitive, which are antisymmetric, and which are irreflexive. 4. Let R be the relation on N defined by IRy ifx and y share a common factor other than 1. Determine the reflexivity and transitivity of R.
Question 1. Draw a digraph for cach of the following relations.
(a) Let A = {a, b. c, d) and let R ((a, b), (b, d). (a, d). (d, a), (d, b),
(b, a), (c. c)}.
(b) Let A= {1, 2. 3, 4, 5, 6, 7, 8} and let x Ry whenever y is divisible by x.
(c) Let A = {1, 2, 3, 4, 5, 6, 7, 8) and let x Ry whenever x and y share no
common factor other than 1
Question 2. Determine which of the relations given in Exxercise I are reflexive, which are
symmetric, which are transitive, which are antisymmetric, and which are
irreflexive.
Question 4.Let R be the relation on N defined by x Ry ifr and y share a common factor
other than 1. Determine the refexivity and transitivity of R.
Question 7. Find the matrix that represents each of the relations given in Question 1.
Question 8. Draw the digraph of the relation defined on {aj, az, a3, a, by the matrix
a d2 d3 d4
a0 01 I11
a2 0 0 I1
a3 1 00
a1 0 0 0
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
