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Magazine Problem 1
Consider the relation \(R=\\{(a, a),(b, b),(c, c),(d, d),(a, b),(b, a)\\}\) on set \(A=\\{a, b, c, d\\}\) Is \(R\) reflexive? Symmetric? Transitive? If a property does not hold, say why.
Problem 1
List all the partitions of the set \(A=\\{a, b\\}\). Compare your answer to the answer to Exercise 5 of Section 11.3 .
Problem 1
Let \(A=\\{0,1,2,3,4,5\\} .\) Write out the relation \(R\) that expresses \(>\) on \(A .\) Then illustrate it with a diagram.
Problem 1
Write the addition and multiplication tables for \(\mathbb{Z}_{2}\).
Problem 1
Let \(A=\\{1,2,3,4,5,6\\},\) and consider the following equivalence relation on \(A\) : \(R=\\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(2,3),(3,2),(4,5),(5,4),(4,6),(6,4),(5,6),(6,5)\\} .\) List the equivalence classes of \(R\).
Problem 2
Write the addition and multiplication tables for \(\mathbb{Z}_{3}\).
Problem 2
Let \(A=\\{1,2,3,4,5,6\\}\). Write out the relation \(R\) that expresses | (divides) on \(A\). Then illustrate it with a diagram.
Problem 2
Let \(A=\\{a, b, c, d, e\\} .\) Suppose \(R\) is an equivalence relation on \(A .\) Suppose \(R\) has two equivalence classes. Also \(a R d, b R c\) and \(e R d\). Write out \(R\) as a set.
Problem 2
Consider the relation \(R=\\{(a, b),(a, c),(c, c),(b, b),(c, b),(b, c)\\}\) on the set \(A=\\{a, b, c\\}\). Is \(R\) reflexive? Symmetric? Transitive? If a property does not hold, say why.
Problem 2
List all the partitions of the set \(A=\\{a, b, c\\}\). Compare your answer to the answer to Exercise 6 of Section 11.3 .
