MTH405 Assignment 1 Solution and Discussion


  • Cyberian's Gold

    Assignment # 1 MTH405 (Fall 2019)

    Total Marks: 10
    Due Date: November 25, 2019.

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    1. Show that the operation which is defined by
      a76bdb5c-32d4-48fc-917d-965cd4daf767-image.png
      is NOT a binary operation on N.

    2. Show that the set fbafc6b9-c88d-49e2-8d4c-bf3d558f731c-image.png is a group under the binary operation of multiplication.


  • Cyberian's Gold

    @zareen said in MTH405 Assignment 1 Solution and Discussion:

    Show that the operation which is defined by

    is NOT a binary operation on N.

    Q. 1 Solution:

    When x + y is less than xy, then x + y - xy does not belong to N.

    So it is not a binary operation on N.

    Show that the set fbafc6b9-c88d-49e2-8d4c-bf3d558f731c-image.png is a group under the binary operation of multiplication.

    Q. 2 Solution:

    ec6445ed-0169-4c89-80d0-895262fc6049-image.png

    93643cde-f437-47ce-bd11-280b9c654e27-image.png

    Hence G ={1,-1} is a group , since all the axioms of the group are satisfied on G={1,-1} with respect to binary operation multiplication.


  • Cyberian's Gold

    @zareen said in MTH405 Assignment 1 Solution and Discussion:

    Show that the operation which is defined by

    is NOT a binary operation on N.

    Q. 1 Solution:

    When x + y is less than xy, then x + y - xy does not belong to N.

    So it is not a binary operation on N.

    Show that the set fbafc6b9-c88d-49e2-8d4c-bf3d558f731c-image.png is a group under the binary operation of multiplication.

    Q. 2 Solution:

    ec6445ed-0169-4c89-80d0-895262fc6049-image.png

    93643cde-f437-47ce-bd11-280b9c654e27-image.png

    Hence G ={1,-1} is a group , since all the axioms of the group are satisfied on G={1,-1} with respect to binary operation multiplication.



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