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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.1: Parabolas

Problem 68E

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=
{(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)}
Draw the directed graph of the relation R
X= {1,2,3,4}.

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Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
Identify the directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}.
Draw a directed graph (digraph) for the relation on {1,2,3,4} {(1,1), (1,4), (2,2), (3,3), (4,1)
Represent the following relation {1,2, 3, 4} with a matrix. {(1,1), (1, 4), (2, 2), (3, 3), (4, 1)}
Verify the relations (5).
Let A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P),(R, P), (S, Q), (S, R)}. Find B^2 (pairs of towns that are connected by two streets). Find B^3(pairs of towns that are connected by three streets). You must use directed graph to findthe answer.
For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2), (3,3), (4,4)} {(1,2), (2,3), (3,4)} {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)} {(2,4), (4,2)} {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}
Represent the relations on {1, 2, 3, 4} with a matrix and digraphs. (The rows and columns correspond to the integers listed in increasing order). {(1, 1), (1, 4), (2, 2), (2, 3), (3, 1), (3. 2), (4, 2), (4, 3)}
Draw a directed graph for the relation R on the set {0, 1, 2, 3} given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.
Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A={1,2,3}. Select one: O a. ={(2,2),(3,1),(2.2).(2,3).(3,3)}. O b. ={(1,1),(3,1),(2.2),(2,3),(3,3)}. O c. =((1,3),(3,1).(2,2), (2,3),(3,3)}. O d. ={(1,2),(1,3).(2,2),(2,3),(3,3)}. O e. ={(1,2),(3,1),(2,2),(2,3),(3,3)}.
Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on theset {1, 2, 3, 4} that is reflexive, symmetric and transitive.
Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation {(2,1),(3,1),(3,2),(4,2)}. Find S◦R.

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