Let R be a binary relation on A={1,2,3,43 defined a is related with b) if a²-b² is divisble by 3. aRb (1.c., by Determine whether (4,2) ER. Show your work. Give a pair (a, b) of natural numbers in A such that (a,b) & R. Explain your answer O Determine whether R is reflexive or not. If so, prove it, if not give a counter example.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4.) Let R be a
binary
relation on A = {1, 2, 3, 43 defined
3₂
by aRb (1.c.,
aRb (1.c., a is related with b) if a²-b2 is divisble by 5.
a) Determine whether (4,2) ER. Show your work.
b) Give a pair (a, b) of natural numbers in A such that
(a,b) & R. Explain your answer
c) Determine whether R is reflexive or not. If so, prove it,
if not
give a
counter example.
d) Determine whether R is antisymmetric
Prove it, if not give a counter example.
e) Determine whether R is transitive or
If not
give a counter example
6r
not. If so,
not. If so, prove it
Transcribed Image Text:4.) Let R be a binary relation on A = {1, 2, 3, 43 defined 3₂ by aRb (1.c., aRb (1.c., a is related with b) if a²-b2 is divisble by 5. a) Determine whether (4,2) ER. Show your work. b) Give a pair (a, b) of natural numbers in A such that (a,b) & R. Explain your answer c) Determine whether R is reflexive or not. If so, prove it, if not give a counter example. d) Determine whether R is antisymmetric Prove it, if not give a counter example. e) Determine whether R is transitive or If not give a counter example 6r not. If so, not. If so, prove it
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