3. Let the relation R be defined on the set R by a Rb if a -b is an integer. Is R and equivalence relation? If yes, provide a proof. Consider the equivalence relation in #3. a. What is the equivalence class of 3 for this relation? 1 b. What is the equivalence class of for this relation? 2
Let R be the relation defined on Z (integers): a R b iff a + b is even. R is an equivalence relation since R is: Group of answer choices Reflexive, Symmetric and Transitive Symmetric and Reflexive or Transitive Reflexive or Transitive Symmetric and Transitive None of the above
Let R be the relation defined on Z (integers): a R b iff a + b is even. Then the distinct equivalence classes are: Group of answer choices [1] = multiples of 3 [2] = multiples of 4 [0] = even integers and [1] = the odd integers all the integers None of the above
Please answer all!! 17. (a) Let R be the relation on Z be defined by a R b if a² + 1 = 62 + 1 for a, b e Z. Show that R is an equivalence relation. (b) Find these equivalence classes: [0], [2], and [7]. 8. Let A, B, C and D be sets. Prove that (A x B) U (C x D) C (AUC) Ⓡ (BUD).
2. Consider the relation E on Z defined by E n, m) n+ m is even} equivalence relation (a) Prove that E is an (b) Let n E Z. Find [n]. equivalence relation in [N, the equivalence class of 3. We defined a relation on sets A B. Prove that this relation is an (In this view, countable sets the natural numbers under this equivalence relation). exactly those that are are 2. Consider the relation E on Z defined by...
Let R be the relation defined on Z (integers): a R b iff a + b is even. Suppose that 'even' is replaced by 'odd' . Which of the properties reflexive, symmetric and transitive does R possess? Group of answer choices Reflexive, Symmetric and Transitive Symmetric Symmetric and Reflexive Symmetric and Transitive None of the above
Let S = Z and R be the relation defined by R = {Z times Z - (n, n)|n Element Z}. (a) Define the relation R, that is aRb if and only if ..... (b) Prove that R^2 = Z times Z
Let R be the equivalence relation defined by aRb if a^2=b^2 (mod5) . Show that the relation is transitive. Also, determine the distinct equivalence classes.
Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R b if Let H-{2m : m ajbe H. (a) Show that R is an equivalence relation. (b) Describe the elements in the equivalence class [3] Z). A relation R is defined on the set Q+ of positive rational numbers by R...
3. (8 points) Let R be the relation defined on Z as follows: For every m,n ez, m Rn4|(m– n). Is R an equivalence relation? If so, prove it. If not, explain which properties of an equivalence relation fails by providing a counterexample for each property that is not satisfied.