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Show your work, please 3. Relations - No Proofs! Determine (no proof needed!) whether each of...
Show your work, please
3. Relations - No Proofs! Determine (no proof needed!) whether each of the following relations R, S, T on the set of real numbers is reflexive, symmetric, antisymmet- ric, and/or transitive. a) x Ry iff 3 - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) xSy iff 2 = 2y: reflexive: symmetric anti-symmetric: transitive: c) Ty iff zy 30: reflexive: symmetric: anti-symmetric transitive:
probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R =...
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
4. Let S be the set of continuous function f: [0;1) ! R. Let R be...
4. Let S be the set of continuous function f: [0;1) ! R. Let R be the relation defined on S by (f; g) 2 Rif(x) is O(g(x)). (a) Is R reflexive? (b) Is R antisymmetric? (c) is R symmetric? (d) is R transitive? Explain your answer in details. Use the definition of big-O to justify your answer if you think R has a certain property or give a counter example if you think R does not have a certain...
F1. need help solving this problem. 1. (25 pts) Here's a neat theorem. Suppose that f la, b] [a, b] is continuous; then f will always map some s-value to itself (a so-called fixed point): i.e....
F1.
need help solving this problem.
1. (25 pts) Here's a neat theorem. Suppose that f la, b] [a, b] is continuous; then f will always map some s-value to itself (a so-called fixed point): i.e. 3 c E (a, b) for which f(c)-c (a) Give a "visual proof" of this theorem. Hint: take your inspiration from our "visual proofs" of Theorem 15 and IVT And notice here that the domain and range of f are the same interval; this...
(5 pts) Give an example of a relation on a set that is a) both symmetric...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
please do question 4. Note that we follow the convention of denoting the set of attributes...
please do question 4.
Note that we follow the convention of denoting the set of attributes {A, B, C} by ABC when we write FDs but not when we write schemas. Given the following set set F of FDs on schema R= (A, B, C, D, E,G): A + BC AB + CD B +C E →D G +C EG → AD Answer the following questions. Questions 1-4 require a formal proof or disproof. A proof may be given either...
Please help me solve 3,4,5 3- For all n € N, let an = 1. Let...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
specifically on finite i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at le...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
I need to answer #3 could be done in only one way, we see that if...
I need to answer #3
could be done in only one way, we see that if we take the table for G and rename the identity e, the next element listed a, and the last element b, the resulting table for G must be the same as the one we had for G. As explained in Section 3, this renaming gives an isomorphism of the group G' with the group G. Definition 3.7 defined the notion of isomorphism and of...
real analysis 1,2,3,4,8please 5.1.5a Thus iff: I→R is differentiable on n E N. is differentiable on / with g'...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
Show your work, please
3. Relations - No Proofs! Determine (no proof needed!) whether each of the following relations R, S, T on the set of real numbers is reflexive, symmetric, antisymmet- ric, and/or transitive. a) x Ry iff 3 - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) xSy iff 2 = 2y: reflexive: symmetric anti-symmetric: transitive: c) Ty iff zy 30: reflexive: symmetric: anti-symmetric transitive:
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
4. Let S be the set of continuous function f: [0;1) ! R. Let R be the relation defined on S by (f; g) 2 Rif(x) is O(g(x)). (a) Is R reflexive? (b) Is R antisymmetric? (c) is R symmetric? (d) is R transitive? Explain your answer in details. Use the definition of big-O to justify your answer if you think R has a certain property or give a counter example if you think R does not have a certain...
F1.
need help solving this problem.
1. (25 pts) Here's a neat theorem. Suppose that f la, b] [a, b] is continuous; then f will always map some s-value to itself (a so-called fixed point): i.e. 3 c E (a, b) for which f(c)-c (a) Give a "visual proof" of this theorem. Hint: take your inspiration from our "visual proofs" of Theorem 15 and IVT And notice here that the domain and range of f are the same interval; this...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
please do question 4.
Note that we follow the convention of denoting the set of attributes {A, B, C} by ABC when we write FDs but not when we write schemas. Given the following set set F of FDs on schema R= (A, B, C, D, E,G): A + BC AB + CD B +C E →D G +C EG → AD Answer the following questions. Questions 1-4 require a formal proof or disproof. A proof may be given either...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
I need to answer #3
could be done in only one way, we see that if we take the table for G and rename the identity e, the next element listed a, and the last element b, the resulting table for G must be the same as the one we had for G. As explained in Section 3, this renaming gives an isomorphism of the group G' with the group G. Definition 3.7 defined the notion of isomorphism and of...
real analysis
1,2,3,4,8please
5.1.5a
Thus iff: I→R is differentiable on n E N. is differentiable on / with g'(e) ()ain tained from Theorem 5.1.5(b) using mathematical induction, TOu the interal 1i then by the cho 174 Chapter s Differentiation ■ EXERCISES 5.1 the definition to find the derivative of each of the following functions. I. Use r+ 1 2. "Prove that for all integers n, O if n is negative). 3. "a. Prove that (cosx)--sinx. -- b. Find the derivative...
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