Let A = {1, 2, 3, 4} and R be a relation on the set A defined by: R = {(1, 1), (
ID: 2964008 • Letter: L
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, 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
Given set A = {1, 2, 3, 4} and relation set, R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 2), (4, 4)}
The R is reflexive. Because for each element of A, there are (1, 1), (2, 2), (3, 3), (4, 4) in R.
The R is not irreflexive. Because there are (1, 1), (2, 2), (3, 3), (4, 4) in R.
The R is not symmetric. Because for (1, 4), there is no (4, 1). Again for (4, 2) there is no (2, 4).
The R is not antisymmetric. Because there are (1, 2), (2, 1). But 1 not equal 2.
The R is not asymmetric. Because there are (1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4).
The R is not transitive. Because there are (4, 2), (2, 1), but there is not (4, 1) in R.
2).
a). As the hashing is done with mod 61, there will be 61 linked list starting from 0 to 60.
b). h(158686)
The value after hashed = (158 + 686) mod 61 = 844 mod 61 = 51.
c). h(328981)
The value after hashed = (328 + 981) mod 61 = 1309 mod 61 = 28.
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