1. For the following, each relation R is defined on the set A. Determine if R is a tree, if it is, find theroot.a) A= {a, b, c, d, e}; R = {(a, d), (b, c), (c, a), (d, e)}b) A = {a, b, c, d, e, f); R = {(a, b), (c, e), (f, a), (f, c), (f, d)}c) A= {1, 2, 3, 4, 5, 6); R = {(1, 1), (2, 1), (2, 3), (3, 4), (4, 5), (4, 6)}d) A= (t, u, v, w, x, y, z}; R = {(t, u), (u, w), (u, x), (u, v), (v, z), (v, y)}79°F Mostly clear%23L89

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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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Consider the following set of ordered pairs of the elements of a set A = {1, 2, 3,4} of numbers and a set B = {a, b, c, d} of letters. {(1, d), (2, d) , (3, a), (2, c), (4, b)} Select all options true of this set. This is not a map from A to B. This is a map from A to B and is onto. This is a map from A to B and is one-to-one. This is a map from A to B and is neither one-to-one nor onto. Map Properties II Consider the following set of ordered pairs of the elements of a set A = {1, 2, 3, 4} of numbers and a set B = {a, b, c, d} of letters. {(1, a), (2, b) , (3, a) , (4, d)} Select all options true of this set. This is not a map from A to B. This is a map from A to B and is onto. This is a map from A to B and is one-to-one. This is a map from A to B and is neither one-to-one nor onto.
) 14. Draw the Hasse diagram for the relation C on the set P({1,2,3}).
If x= 1.3 3+ 3.6 1.3.5 3.6.9 + 1.3.5.7 3.6.9.12 + then P.T-9₂₁²³+24x=11
Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16. Determine: |B|: Number of relations from A to B:
Consider following five sets: 1. { , } { } II. { } II. IV. { , , } V. { , } Find all linearly dependent set(s). (a) I (b) I and IV (c) I and II (d) III, IV and V (e) II (f) II
Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly independent set(s). (a) I (b) I and IV (c) I and II (d) II, IV and V (e) II (f) II
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1. We are given the sets S and V: S = {Anne, Theo} V {studies, runs, meditates} = (a) Find the Cartesian Product of S and V: S x V (b) A relation R. is a subset of the Cartesian product. Create such a subset RC (S X V) with three elements.
6. Q6; Relations (a) Define relations S and R on the set A = {a, b, c, d} as follows: {(a, b), (b, c), (c, d), (b, b)}, S = R = {(b, a), (c, c), (a, c), (d, b)}. i. Find So S, So R, R-o So R. Is R-lo SoR= S ? ii. Determine which of S, R, So R, S-1 or R-1 is a function. (b) Let R = {(x, y) E R × R : 1
This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, RUS = {(x, y) E AXB I (x, y) ER or (x, y) E S} RNS = {(x, y)E AXB| (x, y) ER and (x, y) Es}. Let A = {-2, 2, 3, 5} and B = {2, 3} and define relations R and S from A to B as follows: For every (x, y) E Ax B, x R y - |x| = lyl and xsyex - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RU S, and RN s. (Enter your answers as comma-separated lists of ordered pairs.) AXB = R = S = RUS = ROS =
Given a relation R, we define two sets, the domain of R and the range of R as follows: dom(R) =df {z : for some y, (z, y) E R} ran(R) =df {z : for some x, (x, z) E R}
Suppose A and B are two finite sets such that |B| = |A| - 1 and the number of relations on A is 512. Determine: |B|: Number of relations from B to A:

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1. For the following, each relation R is defined on the set A. Determine if R is a tree, root. a) A= {a, b, c, d, e}; R = {(a, d), (b, c), (c, a), (d, e)}