In Q1-Q4 prove why each relation has or does not have theproperties: reflexive, symmetric, anti-symmetric, transitive.1) Let A = { set of all people }, relation R: A x A whereR= { (a,b) | a,bEA, a is at least as táll as b}2) Set S = {0,1,2,3}, relation R: Sx S is'defined as:(m,n) ER if m + n = 4;3) Z is the set of integers. Relation R: Zx Z is defined as:x,y e Z; (x,y) E R, x is a multiple of y;4) Z* is the set of positive integers, relation R: Z*x Z*, a,b,c,de Z*;(a,b).(c,d) ER if an only if a +d = b + c.5) R and S are relations on set A = {1,2,3,4}, defined asR = {(1,2},(1,3),(2,3).(2,4),(3,1)}; S = {(2,1}.(3,1).(3,2).(4,2)}.Find So R, R o S, R1, S1,where o means composition.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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1(b). Is (p->q)->[(p->q)->q] a tautology? Why or why not? (c). Given the relation on the set . What is the minimum number of ordered pairs which when added to make it an equivalence relation?Discuss your reasoning.
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State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric, and Transitive. Then construct three small worlds showing, respectively, that a relation can be Reflexive and not Symmetric, Symmetric and not Transitive, and Reflexive and not Transitive. Finally, for each of the three small worlds that you construct, give an example of a relation in ordinary language that works like the relation in the small world you built. That is, for your first small world, give an ordinary language example of a relation that is Reflexive and not Symmetric.
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
part b and c
15 Part 2 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R6 = {(a, b) ER² | a b), the unequal to relation For these relations on the set of real numbers, find R₁⁰ R₁. Multiple Choice O O R₁ O R4
17 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) € R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R₁ = {(a, b) € R² | a‡ b), the unequal to relation For these relations on the set of real numbers, find R₁ R6. Multiple Choice O O о R5 R² R6
Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the following are true: ● • (5,0) = R; (8, 6) # R; |[1] R = 2. ●
Determine whether the relation ? on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (?, ?) ∈ ? if and only ifa) ? is taller than ?b) ? and ? have a common grandparent
Question Number 06 a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an equivalence relation. R = {(1,3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} b) Determine whether the graph is bipartite. od c) Draw these graphs i) W; ii) K4
Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is not irreflexive. (2) If a relation on a nonempty set is not reflexive, then it is irreflexive O Neither (1) nor (2) is always true. O Only (1) is always true. O Only (2) is always true. Both (1) and (2) are always true.
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In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A xA where R = { (a,b) | a,b EA, a is at least as tall as b}