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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2005

  • question_answer
    In the group (0,1, 2, 4, 5} under addition modulo 6 a subgroup is :

    A)  { 0, 2, 5}              

    B)  ( 1, 4, 5}

    C)  ( 0, 1, 3)              

    D)  ( 0..2, 4}

    Correct Answer: D

    Solution :

    Composition table of group G is
    \[{{+}_{6}}\] 0 1 2 4 5
    0 0 1 2 4 5
    1 1 2 3 5 0
    2 2 3 4 0 1
    4 4 5 0 2 3
    5 5 0 1 3 4
    It is clear from the table that the set A = { 0, 2, 4} satisfies all the conditions (i) A is closed w.r.t. addition modulo 6. (ii) It also follows associative property \[i.e.,\,\,0{{+}_{6}}(2{{+}_{6}}4)=(0{{+}_{6}}2){{+}_{6}}4\] (iii) \[0\in A\] is the identity element (iv) Inverse of each element exists i.e., Inverse of 0,2, 4 are 0,4,2 respectively By the definition of subgroup, { 0, 2, 4 1 forms a subgroup.


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