# SOLVED MTH405 Assignment 1 Solution and Discussion

• 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 is NOT a binary operation on N.

2. Show that the set is a group under the binary operation of multiplication.

• 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:  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.

• 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:  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.  1

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1

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