MTH405 - Elementary Topics in Pure Mathematics

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 01-10 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 [image: z3f85Wj.png] is NOT a binary operation on N. Show that the set [image: QtLwVol.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 over23-30 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 [image: BwRYFEO.png] is also metric on X. Question No: 2 If d is a metric on X, then show that that [image: t3tXz6J.png] is not metric on X.