Homework Answers
Consider the given relation M.
A person has the same biological mother as herself or himself.
Thus, the relation M is Reflexive.
If person x has the same biological mother as person y, then y has the same biological mother as x.
Thus, the relation M is Symmetric.
If person x has the same biological mother as person y and y has the same biological mother as z, then necessarily the person x has same biological mother z.
Thus, M is transitive.
Therefore, the given relation P is an equivalence relation.
All children of one mother is considered as one equivalence class.
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proofs there isnt anymore info for the question Exercise 5.3.9. For each of the following equivalence...
proofs
there isnt anymore info for the question
Exercise 5.3.9. For each of the following equivalence relations, describe the corre- sponding partition. Your description of each partition should have no redundancy, and should not refer to the name of the relation. (1) Let P be the set of all people, and let be the relation on P defined by x y if and only if x and y have the same mother, for all x,y e P. (2) Let ~...
5. Determine whether the following statements are True or False. Justify your answer with a proof...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the...
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And Heres theorem 10.1 Prove that the relation VR of Theorem 10,1 is an equivalence relation....
And Heres theorem 10.1
Prove that the relation VR of Theorem 10,1 is an equivalence relation. ① show that a group with at least two elements but with no proper nontrivite subgroups must be finite and of prime order. 10.1 Theorem Let H be a subgroup of G. Let the relation ~1 be defined on G by a~lb if and only if albe H. Let ~R be defined by a~rb if and only if ab- € H. Then ~1 and...
Can you #2 and #3? 6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determin...
Can you #2 and #3?
6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determine if it is an equivalence relation on A. If it is, describe the equivalence classes. If it is not determine which properties of an equivalence relation fail. (a) a Hb a and b are the same age in (in years). (b) a Gb a and b have grandparent in common. 2) Consider the relation S(x,y):x...
Determine whether the following statements are True or False. Justify your answer with a proof or...
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if...
1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if and only if m - pis divisible by 3 and n - q is divisible by 5. For example, (2, 19)R(8,4). 1. Identify two elements of N X N which are related under R to (6, 45). II. Is R reflexive? Justify your answer. III. Is R symmetric? Justify your answer. IV. Is R transitive? Justify your answer. V.Is R an equivalence relation? Justify...
Please answer the following questions with solution, thanks 4. Consider the function f(x) = 2x +...
Please answer the following questions with solution, thanks
4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...
For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive....
For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answers for each one. (a) (2 points) The domain is all CPUs. For any CPUs x and y, xRy if x has at least as many cores as y. (b) (2 points) The domain is all people. For any people x and y, xRy if x and y are friends. Assume that everyone is his/her own friend, and that if A...
proofs
there isnt anymore info for the question
Exercise 5.3.9. For each of the following equivalence relations, describe the corre- sponding partition. Your description of each partition should have no redundancy, and should not refer to the name of the relation. (1) Let P be the set of all people, and let be the relation on P defined by x y if and only if x and y have the same mother, for all x,y e P. (2) Let ~...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
And Heres theorem 10.1
Prove that the relation VR of Theorem 10,1 is an equivalence relation. ① show that a group with at least two elements but with no proper nontrivite subgroups must be finite and of prime order. 10.1 Theorem Let H be a subgroup of G. Let the relation ~1 be defined on G by a~lb if and only if albe H. Let ~R be defined by a~rb if and only if ab- € H. Then ~1 and...
Can you #2 and #3?
6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determine if it is an equivalence relation on A. If it is, describe the equivalence classes. If it is not determine which properties of an equivalence relation fail. (a) a Hb a and b are the same age in (in years). (b) a Gb a and b have grandparent in common. 2) Consider the relation S(x,y):x...
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if and only if m - pis divisible by 3 and n - q is divisible by 5. For example, (2, 19)R(8,4). 1. Identify two elements of N X N which are related under R to (6, 45). II. Is R reflexive? Justify your answer. III. Is R symmetric? Justify your answer. IV. Is R transitive? Justify your answer. V.Is R an equivalence relation? Justify...
Please answer the following questions with solution, thanks
4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...
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