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Magazine Problem 56
Using the congruence relation, find the remainder when the first integer is divided by the second. $$1976,9$$
Problem 56
Let \(R\) and \(S\) be relations on a set. Prove each. Let \(A, B, C,\) and \(D\) be any sets, \(R\) a relation from \(A\) to \(B, S\) a relation from \(B\) to \(C,\) and \(T\) a relation from \(C\) to \(D .\) Prove that \(R \odot(S \odot T)=(R \odot S) \odot T\) (associative property)
Problem 57
Find the number of binary relations that can be defined on a set of two elements that are: Reflexive.
Problem 57
\((A, |),\) where \(A=\\{1,2,3,6,9,18\\}\)
Problem 57
Using the congruence relation, find the remainder when the first integer is divided by the second. $$389,276,9$$
Problem 58
Find the number of binary relations that can be defined on a set of two elements that are: Symmetric.
Problem 58
The United Parcel Service assigns to each parcel an identification number of nine digits and a check digit. The check digit is the remainder mod 9 of the 9 -digit number. Compute the check digit for 359,876,015.
Problem 58
\((A, |),\) where \(A=\\{1,2,3,6,8,24\\}\)
Problem 59
Find the number of binary relations that can be defined on a set of two elements that are: Reflexive and symmetric.
Problem 59
Every bank check has an 8 -digit identification number \(d_{1} d_{2} \ldots d_{8}\) followed by a check digit \(d\) given by \(d \equiv\left(d_{1} d_{2}, \ldots, d_{8}\right)\) (7,3,9,7,3,9,7,3) mod \(10,\) where \(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \cdot\left(y_{1}, y_{2}, \ldots, y_{n}\right)=\) \(\sum_{i=1}^{n} x_{i} y_{i} .\) (It is the dot product of the two \(n\) -tuples.) Compute the check digit for 17,761,976.
