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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    Which of the following is a subgroup of\[a=\text{ }\!\!\{\!\!\text{ }0,1,2,3,4,5\text{ }\!\!\}\!\!\text{ },\] under addition modules 6?

    A)  {0, 2}                    

    B)  {0, 1}

    C)  {0, 4}                    

    D)  {0, 3}

    Correct Answer: D

    Solution :

    We prepare a modulo table for all but only \[H=\{0,\,3\}\], satisfies all conditions to be a subgroup of \[{{G}_{1}}=\{0,\,1,\,2,\,3,\,4,\,5,\}\].
    +6 0 3
    0 0 3
    3 3 0
    So, the above table shows that closure law holds in H. Here 0 is the identity and inverse 0, 3 are 0, 3 respectively. Associative law is obviously hold. \[\therefore \] By all these conditions H is subgroup of \[{{G}_{1}}\].


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