d) Determine whether Prove it, if not give Ris e) Determine whether If not Ris antisymmetric a counter example. transitive or give a counter example not. If so, not. If so, prove it,

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

Let A = {a, b, c, d}. How many relations defined on A are re-flexive, symmetric and transitive and contain the ordered pairs (a, b), (b, c), (c, d)?Why?

Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is a factor of b}. Then, show that R is reflexive and transitive but not symmetric.

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