Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations is described by eractly one of the items in the list (i.) – (vi.). Match each relation to the item describing it. You do not need to justify your answers. (a) R1 = {(1,2), (2, 2), (3, 2), (4, 2)} %3D (b) R2 = {(1,1), (1, 2), (1, 3), (1, 4)} (c) R3 = {(1,2), (2, 3), (3, 4), (4, 1)} (d) R4 = {(1,2), (2, 3), (3, 2), (2, 1)} %3D (i.) A reflexive relation (ii.) A symmetric relation iii.) A function that is neither injective nor surjective iv.) An injective but non-surjective function (v.) A bijective function vi.) None of the above
Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations is described by eractly one of the items in the list (i.) – (vi.). Match each relation to the item describing it. You do not need to justify your answers. (a) R1 = {(1,2), (2, 2), (3, 2), (4, 2)} %3D (b) R2 = {(1,1), (1, 2), (1, 3), (1, 4)} (c) R3 = {(1,2), (2, 3), (3, 4), (4, 1)} (d) R4 = {(1,2), (2, 3), (3, 2), (2, 1)} %3D (i.) A reflexive relation (ii.) A symmetric relation iii.) A function that is neither injective nor surjective iv.) An injective but non-surjective function (v.) A bijective function vi.) None of the above
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
C1
![Consider the following relations R1, R2, R3, R4 on the set (4] = {1,2, 3, 4}. Each of the
relations is described by exactly one of the items in the list (i.) – (vi.). Match each relation to the
item describing it. You do not need to justify your answers.
(a) R1 = {(1,2), (2, 2), (3, 2), (4, 2)}
(b) R2 = {(1,1), (1,2), (1, 3), (1, 4)}
(c) R3 = {(1,2), (2, 3), (3, 4), (4, 1)}
%3D
(d) R4 = {(1,2), (2, 3), (3, 2), (2, 1)}
%3D
(i.) A reflexive relation
(ii.) A symmetric relation
(iii.) A function that is neither injective nor surjective
(iv.) An injective but non-surjective function
(v.) A bijective function
(vi.) None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2Fb24d08b2-1a34-4e44-840f-91ca4fb97f8d%2Fof6nsqj_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following relations R1, R2, R3, R4 on the set (4] = {1,2, 3, 4}. Each of the
relations is described by exactly one of the items in the list (i.) – (vi.). Match each relation to the
item describing it. You do not need to justify your answers.
(a) R1 = {(1,2), (2, 2), (3, 2), (4, 2)}
(b) R2 = {(1,1), (1,2), (1, 3), (1, 4)}
(c) R3 = {(1,2), (2, 3), (3, 4), (4, 1)}
%3D
(d) R4 = {(1,2), (2, 3), (3, 2), (2, 1)}
%3D
(i.) A reflexive relation
(ii.) A symmetric relation
(iii.) A function that is neither injective nor surjective
(iv.) An injective but non-surjective function
(v.) A bijective function
(vi.) None of the above
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