SOLVED MTH405 Assignment 1 Solution and Discussion

Assignment # 1 MTH405 (Fall 2019)
Total Marks: 10
Due Date: November 25, 2019.DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
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Show that the operation which is defined by
is NOT a binary operation on N. 
Show that the set is a group under the binary operation of multiplication.


@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 fbafc6b9c88d49e28d4cbf3d558f731cimage.png is a group under the binary operation of multiplication.
Q. 2 Solution:
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.

@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 fbafc6b9c88d49e28d4cbf3d558f731cimage.png is a group under the binary operation of multiplication.
Q. 2 Solution:
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.