Q-4: a) Determine whether the relation R represented by the given matrix is a partial order: -1 0 MR = [aij.] = 1 0001 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1- b) Find, if exists, the inverse of the function f: zz, where f(n) = n mod 10. c) Show that f: R → R defined as f(a) = 3a³-4 is a one to one

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Q-4:
a) Determine whether the relation R represented by the given
matrix is a partial order:
1 0
0 01
1 0 0 0
1
MR = [a;j] =
1
1
1
1
1
0 0 0
1 0
Lo o o 1 1-
b) Find, if exists, the inverse of the function f: z → Z, where
f(n) = n mod 10.
c) Show that f : R → R defined as f(a) = 3a³- 4 is a one to one
function.
Transcribed Image Text:Q-4: a) Determine whether the relation R represented by the given matrix is a partial order: 1 0 0 01 1 0 0 0 1 MR = [a;j] = 1 1 1 1 1 0 0 0 1 0 Lo o o 1 1- b) Find, if exists, the inverse of the function f: z → Z, where f(n) = n mod 10. c) Show that f : R → R defined as f(a) = 3a³- 4 is a one to one function.
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