Let R = {(a, a),(a, b), (b, b),(a, c), (c, c)} be a partial order relation on Σ= {a,b,c}. Let ≤ be the corresponding lexicographic order on Σ, the set of all finite strings over Σ. Which of the following is true? Select one: O a. abbac ≤ abbab O b. abbac ≤ abbaac O c. bc ba O d. O e. abbaaacc = abbaab abbacs abb

Q: Consider the set A = {2, 3, 5, 11, 12, 13} and the relation Va, b E A, a R b → a = b mod 3. List all…

A: Given the set, A=2, 3, 5, 11, 12, 13 and the relation ∀a,b∈A, a R b↔a≡b mod 3

Q: 4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants…

A: Given that, A is the set of all animals, E is the set of all elephants and F is the set of all frogs…

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: Let A be the set of all citizens of New York City. For a, b E A, define a ~ -b if and only if ●…

A: To show that ~ defines an equivalence relation on the set A (the set of all citizens of New York…

Q: ame programs. A = the set of all people in the Social Security database; a Rb if and only if a and b…

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Q: Let U={1,2,3,4,5,6} be the universal set and A-{2,4,6}. Then the power set of the complement of U…

A: Given that  U={1,2,3,4,5,6} and A={2,4,6} To find The power set of the complement of U.

Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: (c) Consider the equivalence relation R on the set X = {1,2,3,4,5,6,7} given by R = {(1,1),(1,6),…

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Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: c) Let R be a binary relation on the set of ordered pairs of integers such that ((a,b), (c,d)) = R…

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Q: Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10),

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Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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Q: (i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements…

A: Given that S and T are equivalence relation on a set B. i ) the equivalence class [b] determined by…

Q: Let R and S be relations defined on the set of {8, 1, 2, 7}. R = {(1,8), (7, 8), (8, 1), (7, 7)}. S…

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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: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

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Q: Considering A as a set which contains the elements {2,3,4,5,6,7,8}, Define a relation R from A to A…

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Broadly speaking, what is a mathematical closure? O A. Only relations have closures. They are…

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Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Let S = ((a), b, (a, (b)]), c). Which one of the following relations on S is a strict partial order?…

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Q: a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an…

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Q: B. Determine the power set of the set A= {2,8,10}. C. Let the relation R be {(1,5), (5,9), (8,1)}.…

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Q: aRb, cRd and aRd, then bRc.

A: A relation R defined on a set A is i) reflexive if aRa for all a belonging to A.ii) symmetric if aRb…

Q: (b) The domain is fa, b, e, d, e, f). The relation is the set: (b, e), (b, d). (c, a), (c. S). (a,…

A: Given: The relation of a set a, b, c, d, e, f is b, e, b, d, c, a, c, f, a, f, a, a, b, b, c, c, d,…

Q: Suppose p and o are relations defined on S = {1, 2, 3, 4} by the sets p = {(2, 2), (3, 2), (3, 4),…

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Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: Consider the subset relation C on the power set of {a,b,c}, that is P{a,b,c}. (a) Construct the…

A: Let S be a partially ordered set. Use the following definitions, to obtain the solution. Let a,b∈S…

Q: Ris an equivalence relation on a set with 5 elements. Which of the following are possible? There are…

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Q: Discrete mathematics

A: Partial ordering relation

Q: Write down all of the properties that each of the following binary relations satisfies from among…

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Q: 1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S,…

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Q: Consider the "divides" relation on the set A = {1, 2, 3, 5, 6, 7, 8, 10, 20, 30, 60, 70} (a) Draw…

A: A Hassen diagram is a graphical representation of the relation of elements of a partially ordered…

Q: Let U= {1,2,. 1} be the universal set. Let A={x|x eU,x is a multiple of 6, B={x\xeU,xis a multiple…

A: Given: U={1,2,...16} A={x|x∈U, x is a multiple of 6} B={x|x∈U, x is a multiple of 5}…

Q: 1(b). Is (p->q)->[(p->q)->q] a tautology? Why or why not?  (c). Given the relation on the set .…

A: We are entitled to solve only one question at a time. Please submit another question separately. To…

Q: Consider the set S = {A, B, C, D}: For each of the following relations on S, determine whether it is…

A: Definitions: