Let A = {1, 2, 3, 4} and R be a relation on the set A defined by: R - {(1.1). (1

Question

Let A = {1, 2, 3, 4} and R be a relation on the set A defined by: R - {(1.1). (1,2), (1,4), (2,1), (2,2), (3,3), (4,2), (4,4)}. Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive Suppose an online retailer identifies each member with a 6-digit account number. Define the hashing function h, which takes the first 3 digits of an account number as 1 number and the last 3 digits as another number, adds them, and then applies the mod-61 function. How many linked lists does this create? Compute h(158686) Compute h(328981)

Explanation / Answer

1.

it is reflexive, (since (1,1),(2,2),(3,3),(4,4) belongs to R)

asymmetric(since (1,4) belongs to R but not(4,1)),

not anti symmetric (since (1,2) and (2,1) belongs to R)

not transitive (since (2,1), (1,4) belongs to R but not (2,4))

2.

(b)

158+686 = 844 = 51 (mod 61)

=>

h(158686) = 51

(c)

328 +981 = 1309 = 28(mod 61)

=>

h(328981) =28

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