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Let G = {n ε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1 - {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }
Q. which one of the following is TRUE?
Q. which one of the following is TRUE?
- a)S1 is a subgroup of G but S2 is NOT a subgroup of G
- b)S1 is NOT a subgroup of G but S2 is a subgroup of G
- c)Both Sl and S2 are subgroups of G
- d)Neither S1 nor S2 is a subgroup of G
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multipl...
Given G = {n ε Z : 1 ≤ n ≤ 55, g.c.d(n, 56) = 1}
i.e. G = {1, 2, 5, 9,11, 13, 15, 17, 19,23,25,27, 2 9 ,3 3 ,3 7 ,3 9 ,4 1 ,4 3 ,4 5 ,4 7 ,5 1 ,5 3 ,5 5 }
i.e. G is finite abelian group.
Here, S1 = {1, 9 , 17 , 25, 33, 41}.
So, S1 is a subgroup of G because S, satisfies all properties of subgroup of G. i.e., closure , associative existence of id entity and existence of inverse.
S2 = {1,15, 29,43} is also subgroup of G.
Hence, Both S1 and S2 are subgroups of G.
i.e. G = {1, 2, 5, 9,11, 13, 15, 17, 19,23,25,27, 2 9 ,3 3 ,3 7 ,3 9 ,4 1 ,4 3 ,4 5 ,4 7 ,5 1 ,5 3 ,5 5 }
i.e. G is finite abelian group.
Here, S1 = {1, 9 , 17 , 25, 33, 41}.
So, S1 is a subgroup of G because S, satisfies all properties of subgroup of G. i.e., closure , associative existence of id entity and existence of inverse.
S2 = {1,15, 29,43} is also subgroup of G.
Hence, Both S1 and S2 are subgroups of G.
Most Upvoted Answer
Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multipl...
Given G = {n ε Z : 1 ≤ n ≤ 55, g.c.d(n, 56) = 1}
i.e. G = {1, 2, 5, 9,11, 13, 15, 17, 19,23,25,27, 2 9 ,3 3 ,3 7 ,3 9 ,4 1 ,4 3 ,4 5 ,4 7 ,5 1 ,5 3 ,5 5 }
i.e. G is finite abelian group.
Here, S1 = {1, 9 , 17 , 25, 33, 41}.
So, S1 is a subgroup of G because S, satisfies all properties of subgroup of G. i.e., closure , associative existence of id entity and existence of inverse.
S2 = {1,15, 29,43} is also subgroup of G.
Hence, Both S1 and S2 are subgroups of G.
i.e. G = {1, 2, 5, 9,11, 13, 15, 17, 19,23,25,27, 2 9 ,3 3 ,3 7 ,3 9 ,4 1 ,4 3 ,4 5 ,4 7 ,5 1 ,5 3 ,5 5 }
i.e. G is finite abelian group.
Here, S1 = {1, 9 , 17 , 25, 33, 41}.
So, S1 is a subgroup of G because S, satisfies all properties of subgroup of G. i.e., closure , associative existence of id entity and existence of inverse.
S2 = {1,15, 29,43} is also subgroup of G.
Hence, Both S1 and S2 are subgroups of G.
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Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multipl...
A monoid is a semigroup that has an identity element. In a monoid, there exists an element (the identity) such that combining it with any other element in the set leaves the other element unchanged under the specified binary operation.
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Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer?
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Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer?.
Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let G = {nε Z : 1 ≤ n ≤ 55, gcd(n, 56) = 1} be a multiplicative group modulo 56. Consider the sets S1- {1,9, 17,25,33,41} and S2 = { 1 ,1 5 ,2 9 ,43 }Q.which one of the following is TRUE?a)S1is a subgroup of G but S2 is NOT a subgroup of Gb)S1is NOT a subgroup of G but S2 is a subgroup of Gc)Both Sl and S2 are subgroups of Gd)Neither S1nor S2 is a subgroup of GCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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