Let A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1, b), (3, a), (3, b), (4, c)} and S = {(a, y), (c, x), (a, z)} (i) Draw the diagrams of R and S. (ii) Find the matrix of each relation R, S (composition) RoS. (iii) Write R −1 and the composition RoS as sets of ordered pairs. (b) Find x and y where: (i) (x + 2, 4) = (5, 2x + y); (ii) (y − 2, 2x + 1) = (x − 1, y + 2)
Let A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1, b), (3, a), (3, b), (4, c)} and S = {(a, y), (c, x), (a, z)} (i) Draw the diagrams of R and S. (ii) Find the matrix of each relation R, S (composition) RoS. (iii) Write R −1 and the composition RoS as sets of ordered pairs. (b) Find x and y where: (i) (x + 2, 4) = (5, 2x + y); (ii) (y − 2, 2x + 1) = (x − 1, y + 2)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...
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Let A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}.
Consider the relations R from A to B and S from B to C as follows:
R = {(1, b), (3, a), (3, b), (4, c)} and S = {(a, y), (c, x), (a, z)}
(i) Draw the diagrams of R and S.
(ii) Find the matrix of each relation R, S (composition) RoS.
(iii) Write R
−1
and the composition RoS as sets of ordered pairs.
(b) Find x and y where:
(i) (x + 2, 4) = (5, 2x + y);
(ii) (y − 2, 2x + 1) = (x − 1, y + 2)
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