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Let A 1,2,3,4, 5, 6] How many equivalence relations on A have (a) exactly two equivalence classes of size 3 (b) exactly...
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 e...
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for ...
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on...
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.
For questions 16-18, what are the equivalence classes. Pls say how many eqivalence classes are fo...
For questions 16-18, what are the equivalence classes. Pls say
how many eqivalence classes are for each.
Thank you in advance, but completed with in the hour would be
greatly apreciated bc I have an exam, and I will obviously like any
completed work. Hope you all have a great day!
Example. Let R-{(a, b) E Z x Ζ : lal-lol}, for era mple: 2R-2) and 4R4 but 43. We see that R is an equivalence relation on Z. First,...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
Problem 5. Equivalence classes really separate elements in A in a very strict way. Two different...
Problem 5. Equivalence classes really separate elements in A in a very strict way. Two different equivalence classes are disjoint, altogether they give A back. Working with the defi- nition of equivalence class (R.S,T) and the definition of equivalence class prove the mentioned properties. (a) If a,b € A, then a – b if and only if (a)rn [b]R=. (b) If a, b e A, then if [a]rn (br #0 the [a]R= [b]R (c) For all a € A, (a)r...
Prove that Z/ ≡3 has exactly three elements using the given hint! Definition: Let R be...
Prove that Z/ ≡3 has exactly three elements using the
given hint!
Definition: Let R be an equivalence relation on the set A. The set of all equivalence classes is denoted by A/R (g) Prove that Z/ has exactly three elements. Hint: First, verify that [5]3, [7]3, and [013 are three different elements of Z/-3-Then, verify that every m E Z is in one of these sets. Then explain why those two facts imply that [5]3, [7 3, and [013...
Let us consider 2 sets A = {1,2,3,4} and B = { 5,6}. 1. What is...
Let us consider 2 sets A = {1,2,3,4} and B = { 5,6}. 1. What is {}? 2. What is |A|? 3. What is A union B? 4. What is A intersection B? 5. What is {{}}? 6. What is |{{}}|? 7. What is A x B? 8. What is BxA? 9. If A has 2^5 elements and B has 2^6 elements, how many elements are there in AxB?
How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain...
How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain the ordered pairs (2, 2), (3, 4) and (5, 6)?
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...
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.
For questions 16-18, what are the equivalence classes. Pls say
how many eqivalence classes are for each.
Thank you in advance, but completed with in the hour would be
greatly apreciated bc I have an exam, and I will obviously like any
completed work. Hope you all have a great day!
Example. Let R-{(a, b) E Z x Ζ : lal-lol}, for era mple: 2R-2) and 4R4 but 43. We see that R is an equivalence relation on Z. First,...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
Problem 5. Equivalence classes really separate elements in A in a very strict way. Two different equivalence classes are disjoint, altogether they give A back. Working with the defi- nition of equivalence class (R.S,T) and the definition of equivalence class prove the mentioned properties. (a) If a,b € A, then a – b if and only if (a)rn [b]R=. (b) If a, b e A, then if [a]rn (br #0 the [a]R= [b]R (c) For all a € A, (a)r...
Prove that Z/ ≡3 has exactly three elements using the
given hint!
Definition: Let R be an equivalence relation on the set A. The set of all equivalence classes is denoted by A/R (g) Prove that Z/ has exactly three elements. Hint: First, verify that [5]3, [7]3, and [013 are three different elements of Z/-3-Then, verify that every m E Z is in one of these sets. Then explain why those two facts imply that [5]3, [7 3, and [013...
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...
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