Indicate the partition of the set A = {x integer: 2 ≤ x ≤ 12} resulting from the equivalence relation R on A defined by R = {(x, y) = AXA: x mod 4=y mod4}.O {2, 6, 10}; {3, 7, 11}; {4, 8, 12}; {5, 9}O {1,5,9}; {2, 6, 10}; {3, 7, 11}; {4, 8, 12}O {1,2,3}; {4, 5, 6}; {7, 8, 9}; {10, 11, 12}O {1,3,5}; {2, 4, 6}; {7, 9, 11}; {8, 10, 12}O None of these.

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Answered: Indicate the partition of the set A={ x…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please just answer parts iv. and v.
Consider the relation R = {(a,b) | a is congruent to b mod 3} on set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the equivalence classes of R? O {1, 4, 7, 10}, {2, 5, 8), {3, 6, 9} O {1, 2, 4, 5, 7, 8, 10}, {3, 6, 9} O {1, 5, 9}, {2, 6, 10}, {3, 7}, {4, 8} O {2, 4, 6, 8, 10), (1, 3, 5, 7, 9}
Let X be the set {1, 2, 3, 4, 5} and Rthe "less than" relation on X, that is x Ryif and only if x
2. For each of these relations on the set {1, 2, 3, 4), decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} c) {(2, 4), (4, 2)} d) {(1, 2), (2, 3), (3, 4)} e) {(1, 1), (2, 2), (3, 3), (4,4)} f) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}
3 For the equivalence relation on {0, 1,2,3,4} defined as {(x, y) : x +y is even} (a) Write it out as a list of ordered pairs (b) List the cells in the associated partition.
Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =
6) Let A = {4,5,6} and B = {3,6,7}. Define relations U, V, and W from A to B as follows, For all (x, y) E A×B, (x, y) eU x>y (x, y) e V > X-y is an integer. W = {(4,7), (6,3), (5,6)} Indicate whether any of the relations U, V, and W are functions from A to B.
2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a, b) = (a₁, b₁) if a = a₁. (d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.
9. Let A = {1,2,3,4,5,6}. How many different relations are there on the set A? Consider the subest-A (R_R) ((**) ve PLCD . What feathtar relatio... to tims! Explaine 11. Given a finite set A, how many different relations are there on A? In the following exercises, subsets R of R² =R x R or Z² = Zx Z are indicated by gray shading. In each case, R is a familiar relation on R or Z. State it. 12. A R 13. R 14. 15.
The binary relation {(1,1), (2,1), (2,2), (2,3), (3,1), (3,2)} on the set {1, 2, 3} is O reflexive, symmetric, and transitive transitive O antisymmetric O anstisymmetric and transitive

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