Let P be the set of all positive factors of 90, and let / denote the 'divides' relation. Then the poset (P, /) a Boolean lattice? Justify. 1.

Q: With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 1. Let H = {1, 2, 3, 4, 5} and the rlation RC H², with (a, b) ER + a = b( mod 3). • Give the set R.…

A: R ={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: 4. Suppose R is a relation on a set A. The complementary relation R is defined by letting a R b if a…

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Q: A set of dice is called intransitive (or non-transitive) if it contains three dice, A, B, C, with…

A: There are three dice, which have the following faces: Die A= {2,2,4,4,9,9} Die B= {1,1,6,6,8,8} Die…

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

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Q: 4. Let S = {1, 2,..., 10}. Out of all the equivalence relations on S that have exactly 2 equivalence…

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Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given conditions are met,…

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Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

Q: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…

A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…

Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n 2|(m-n). Show the relation

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Q: tiv Consider the relation defined on Z by m~n if and only if m+n is eve (a) Show that ~ is an…

A: Consider the relation ~ defined on Z by m~n if and only if m+n is even. Now, To show  Relation ~ is…

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A| < [B|…

A: A partial order relation is total order relation if each of the pair of the elements are comparable.…

Q: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

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Q: Let D be the relation on the natural numbers defined by the rule m divides n if and only if m does…

A: Let D be the relation on the natural number is defined by the rule m divides n if an only if m does…

Q: 9. Let R be the relation defind on NxN by (m)R(m2) if and only if m1 – n1 = m2 – n2. Describe the…

A: The equivalence class of an element means a set of all those elements that are related to that…

Q: Consider the set of all members belonging to the same family and the binary relation defined as " to…

A: GIVEN: The set of all members belonging to the same family and the binary relation defined as " to…

Q: Let R be the relation on the set N0 of natural numbers given by the following rule: (n,m)∈R if and…

A: Definition of - (1) A binary relation is an Equivalence Relation on a non-empty set  S  if and only…

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n→2|(m-n). Show the relation S is: (a)…

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Q: 1.What is Relation?…

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Q: Consider the set NXN .e the set of ordered pairs of positile integers. Let I be the relection ~ in…

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an order relation. (b)…

A: Let Ω be a non-empty set. a) To show that the inclusion relation in P(Ω) in an order relation. X,Y ∈…

Q: The equivalence class of -1 for the relation congruence modulo 5 is O {...,-12, –7, –2, 3,8, 13,…

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Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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Q: Consider the set T whose elements are all the factors of 1000 and denote a relation τ ⊂ T × T such…

A: Given Data: Consider the set T whose elements are all the factors of 1000 and denote a relation τ ⊂…

Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

Q: Let K = {A, Ā, A-°, A-o-, A°, A°¯, A°-o}. Show that K is closed under the interior and closure…

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Q: 3. Let S be the congruent modulo 2 relation on Z,that is m S n→ 2|(m-n) . Show the relation

A: A relation is called symmetric if for any  if  then we have .

Q: 3) Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the…

A: Given A=1,2,3,4,5,6,7,8 contains the ordered pair 2,3,3,24,7,5,5 and 8,7 Since, for the diagonal…

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or A=B.

Q: Let S be the congruent modulo 7 relation on Z, that is m Sn 7|(m-n). Show the relation S is: (a)…

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Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is: O…

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Q: Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R…

A: Introduction :Given , R : set of all binary relations on the set {1,2,3}We have asked to find the…

Q: 2) Let A be the set of all integers. Suppose that xRy + x and y have the same reminder when divided…

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Q: A = {1,2,3,4,6,8,12} a.) Relation on Z Refleksif Symmetric Transitive

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Q: 10. Let be the relation defind on Z by „R, if and only if a|b. Orve an explicit description of the…

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Q: Let R be the divisibility relation (|) on A = {3,5, 6,7, 10, 20, 30}. We know that (A, |) is a…

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Q: equivalence

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Q: 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

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Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an crder relation…

A: A partial order relation leads to poset which is very interesting.