Discrete Mathematics Questions

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1) 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), (4, 1), (4, 4)}

Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not.
Reflexive: R is not reflexive since if it were (3,3) should be in R and it is not
Irreflexive: R is not irreflexive: (1,1) is in R.
Symmetric: R is symmetric, since for every pair (x,y) also (y,x) is in R
Assymetric: R is not asymmetric since (2,1) and (1,2) are in R
Antisymmetric: R is not antisymmetric for the same reason: both (2,1) and (1,2) are in R
Transitive: R is transitive since if (x,y) and (y,z) are in R, then also (x,z) is in R.
For example: (4,1) and (1,4) are in R. So is (4,4). Checked for all other cases.

2) Suppose an online retailer identifies each member with a 7-digit account number. Define the hashing function h, which takes the first 4 digits of an account number as one number and the last 3 digits as another number, adds them, and then applies the mod-67 function.
a) How many linked lists does this create? This creates 67 linked lists.
b) Compute h(5716379). 5716+379= 6095=65 (mod 67)
c) Computer h(3842137)= 3842+137= 3979=26 (mod 67)...