
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:
• To solve this assignment, you should have good command over 0110 lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
• Don’t use colorful back grounds in your solution files.
• Use Math Type or Equation Editor etc for mathematical symbols if needed.
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
• Make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.Show that the operation which is defined by
a76bdb5c32d448fc917d965cd4daf767image.png
is NOT a binary operation on N.Show that the set fbafc6b9c88d49e28d4cbf3d558f731cimage.png is a group under the binary operation of multiplication.

Assignment # 2 MTH405 (Fall 2019)
Total Marks: 10
Due Date: January 24, 2020.DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over2330 lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
• Don’t use colorful back grounds in your solution files.
• Use Math Type or Equation Editor etc for mathematical symbols if needed.
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
• Make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.Question No: 1
If d is a metric on X, then show that bec7d1e8309047e99ff98204c8969026image.png is also metric on X.
Question No: 2If d is a metric on X, then show that that a091b36639b44fd38dcbd15770df2067image.png is not metric on X.
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:
• To solve this assignment, you should have good command over 0110 lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
• Don’t use colorful back grounds in your solution files.
• Use Math Type or Equation Editor etc for mathematical symbols if needed.
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
• Make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.
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.