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Let G be the group of non zero real numbers under multiplication
(1) {x ∈ G | x = 1 or x is irrational}
(2) {x ∈ G | x ≥ 1}
  • a)
    Both (1) and (2). Subgroup of G
  • b)
    only (1) is subgroup of G
  • c)
    only (2) is subgroup of G
  • d)
    Neither (1) nor (2) is subgroup of G
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let G be the group of non zero real numbers under multiplication(1) {x...
Let G be the group of nonzero real numbers under multiplication,
H = {x ∈ G | x = 1 or x is irrational} and
K ={x ∈ G | x ≥ 1}then H is not a subgroup of G since 
Also, K is not a subgroup since  
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Most Upvoted Answer
Let G be the group of non zero real numbers under multiplication(1) {x...
In the group G of nonzero real numbers under multiplication, the operation is multiplication. The identity element is 1, since 1 multiplied by any number x gives x. The inverse of any number x is 1/x, since multiplying x by 1/x gives the identity element 1.

The group G is closed under multiplication, since the product of any two nonzero real numbers is also nonzero. Associativity holds because multiplication of real numbers is associative.

Therefore, G is a group under multiplication with the identity element 1 and inverses given by 1/x for any nonzero real number x.
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Community Answer
Let G be the group of non zero real numbers under multiplication(1) {x...
Let G be the group of nonzero real numbers under multiplication,
H = {x ∈ G | x = 1 or x is irrational} and
K ={x ∈ G | x ≥ 1}then H is not a subgroup of G since 
Also, K is not a subgroup since  
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Let G be the group of non zero real numbers under multiplication(1) {x ∈ G | x = 1 or x is irrational}(2) {x ∈ G | x ≥ 1}a)Both (1) and (2). Subgroup of Gb)only (1) is subgroup of Gc)only (2) is subgroup of Gd)Neither (1) nor (2) is subgroup of GCorrect answer is option 'D'. Can you explain this answer?
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Let G be the group of non zero real numbers under multiplication(1) {x ∈ G | x = 1 or x is irrational}(2) {x ∈ G | x ≥ 1}a)Both (1) and (2). Subgroup of Gb)only (1) is subgroup of Gc)only (2) is subgroup of Gd)Neither (1) nor (2) is subgroup of GCorrect answer is option 'D'. 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 be the group of non zero real numbers under multiplication(1) {x ∈ G | x = 1 or x is irrational}(2) {x ∈ G | x ≥ 1}a)Both (1) and (2). Subgroup of Gb)only (1) is subgroup of Gc)only (2) is subgroup of Gd)Neither (1) nor (2) is subgroup of GCorrect answer is option 'D'. 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 be the group of non zero real numbers under multiplication(1) {x ∈ G | x = 1 or x is irrational}(2) {x ∈ G | x ≥ 1}a)Both (1) and (2). Subgroup of Gb)only (1) is subgroup of Gc)only (2) is subgroup of Gd)Neither (1) nor (2) is subgroup of GCorrect answer is option 'D'. Can you explain this answer?.
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