{1,2, 3} under multiplication modulo 4 is not a group. {1,2, 3, 4} under multiplication modulo 5 is a group. The intersection of any two subgroups of a group G is also a subgroup of G.
{1,2, 3} under multiplication modulo 4 is not a group. {1,2, 3, 4} under multiplication modulo 5 is a group. The intersection of any two subgroups of a group G is also a subgroup of G.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Which one of the following multiple-choice questions is incorrect?
![Q 2 Which one of the following is incorrect?
(a) {1,2,3} under multiplication modulo 4 is not a group.
(b) {1,2,3, 4} under multiplication modulo 5 is a group.
(c) The intersection of any two subgroups of a group G is also a subgroup
of G.
(d) {0, 2,4} under addition modulo 8 is a subgroup of (Zg, Os).
Q 3 If a andb are the elements of a group G, then (ba)-1 =
(a) b-'a-1
(b) a-lb-1
(c) a-1b
(d) b-la
Q 4 The inverse of the element (132) of the group S3 under function composi-
tion o is
(a) (12)
(b) (132)
(c) (123)
(d) (23)
Q 5 The order of the element (123) of the group (S3,0) is
(a) 1
(b) 2
(c) 3
(d) o0
Q 6 The order of the group (U(12), 12) is
(а) 12
(b) 11
(c) 6
(d) 4
Q 7 Which one of the following is abelian group?
(a) (S3,0)
(b) {A e Mnxn : det(A) = 1} under matrix multiplication
(c) Any cyclic group
(d) None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bfda294-ae4e-4743-b35d-e22aeed8f953%2Fc87e928a-fd24-4962-9aad-761ef932aa58%2F66fln6x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q 2 Which one of the following is incorrect?
(a) {1,2,3} under multiplication modulo 4 is not a group.
(b) {1,2,3, 4} under multiplication modulo 5 is a group.
(c) The intersection of any two subgroups of a group G is also a subgroup
of G.
(d) {0, 2,4} under addition modulo 8 is a subgroup of (Zg, Os).
Q 3 If a andb are the elements of a group G, then (ba)-1 =
(a) b-'a-1
(b) a-lb-1
(c) a-1b
(d) b-la
Q 4 The inverse of the element (132) of the group S3 under function composi-
tion o is
(a) (12)
(b) (132)
(c) (123)
(d) (23)
Q 5 The order of the element (123) of the group (S3,0) is
(a) 1
(b) 2
(c) 3
(d) o0
Q 6 The order of the group (U(12), 12) is
(а) 12
(b) 11
(c) 6
(d) 4
Q 7 Which one of the following is abelian group?
(a) (S3,0)
(b) {A e Mnxn : det(A) = 1} under matrix multiplication
(c) Any cyclic group
(d) None of the above
![Q 8 Which one of the following is a cyclic group?
(a) (Z,+)
(b) (Q, +)
(c) (R, +)
(d) (R \ {0}, ·)
Q 9 Which one of the following is the smallest subgroup of (Z, +) that contains
2?
(a) (2Z, +)
(b) (4Z, +)
(c) (6Z, +)
(d) None of the above
Q 10 Which one of the following is not a ring?
(a) (Z, +, ·)
(b) (MAx4(R),+,:)
(c) (Z5, O5, 85)
(d) None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bfda294-ae4e-4743-b35d-e22aeed8f953%2Fc87e928a-fd24-4962-9aad-761ef932aa58%2F7wzv505_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q 8 Which one of the following is a cyclic group?
(a) (Z,+)
(b) (Q, +)
(c) (R, +)
(d) (R \ {0}, ·)
Q 9 Which one of the following is the smallest subgroup of (Z, +) that contains
2?
(a) (2Z, +)
(b) (4Z, +)
(c) (6Z, +)
(d) None of the above
Q 10 Which one of the following is not a ring?
(a) (Z, +, ·)
(b) (MAx4(R),+,:)
(c) (Z5, O5, 85)
(d) None of the above
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