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Choose the correct option.

  • a)
    (Q, +) is isomorphic to (R, +).

  • b)
    (R, +) is not isomorphic to (R — {o}, •).

  • c)
    There are two non-isomorphic cyclic group of order 20092009.

  • d)
    There are 20092009 non-isomorphic cyclic groups of order 20092009.

Correct answer is option 'B'. Can you explain this answer?
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Choose the correct option.a)(Q, +) is isomorphic to (R, +).b)(R, +) is...


3. There are two non-isomorphic cyclic groups of order 20092009:



  • A cyclic group of a given order is unique up to isomorphism. There is only one cyclic group of any given order. Therefore, this statement is false.



4. There are 20092009 non-isomorphic cyclic groups of order 20092009:



  • There is exactly one cyclic group of any given order. Therefore, there are not 20092009 non-isomorphic cyclic groups of order 20092009. This statement is false.

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Choose the correct option.a)(Q, +) is isomorphic to (R, +).b)(R, +) is...
, ).
c)(R, ) is isomorphic to (Q, ).
d)(Q, ) is not isomorphic to (Q, ).

The correct option is c) (R, ) is isomorphic to (Q, ).
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Choose the correct option.a)(Q, +) is isomorphic to (R, +).b)(R, +) is not isomorphic to (R — {o}, •).c)There are two non-isomorphic cyclic group of order 20092009.d)There are 20092009 non-isomorphic cyclic groups of order 20092009.Correct answer is option 'B'. Can you explain this answer?
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