(i) Find the number of permutations of the 8 letters of the word SYLLABUS. Find also the number of different selections of 5 letters which can be made from the letters of the word SYLLABUS. (ii) Prove by Mathematical induction the -1X3r-2)=n²(n-1). r= 1 (iii) A relation R is defined on Z, the set of integers, by aRbif and only if a-b is even. Show that R is transitive.
(i) Find the number of permutations of the 8 letters of the word SYLLABUS. Find also the number of different selections of 5 letters which can be made from the letters of the word SYLLABUS. (ii) Prove by Mathematical induction the -1X3r-2)=n²(n-1). r= 1 (iii) A relation R is defined on Z, the set of integers, by aRbif and only if a-b is even. Show that R is transitive.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Question ii, iii & i
![(i) Find the number of permutations of the 8 letters of the word SYLLABUS. Find also the number
of different selections of 5 letters which can be made from the letters of the word SYLLABUS.
(ii) Prove by Mathematical induction the (r-1)3r-2)=n² (n-1).
!!
r= 1
(iii) A relation R is defined on Z, the set of integers, by aRbif and only if a-b is even. Show that R
is transitive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a6d9c67-6f13-49d2-ac4d-2d996f90a88b%2F2e0343b9-a53d-4799-aadc-529e45499bf4%2Fnqywmb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(i) Find the number of permutations of the 8 letters of the word SYLLABUS. Find also the number
of different selections of 5 letters which can be made from the letters of the word SYLLABUS.
(ii) Prove by Mathematical induction the (r-1)3r-2)=n² (n-1).
!!
r= 1
(iii) A relation R is defined on Z, the set of integers, by aRbif and only if a-b is even. Show that R
is transitive.
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