Consider the poset R with relation <. For each S C R, determine sup(S) and inf(S), if they exist. 1. S = {7.1, 7.01, 7.001, ...} 2. S = {r € Q | v2 < r < v3} 3. S = {1+ (-1)" :n eN

Q: Set roster notation of U={r € Z l -2<r<2

A: we have given the set U = {r∈Z,  -2&lt;r&lt;2} we have to write the set roster notation of U The set…

Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: Given a relation g from the set D = {1, 2, 3, 4, 5} to the set C = {a, b, c, d}, where g = {(1, a),…

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Q: Using contradiction method, prove that for every nonempty sets A and B, An (B- A)=0.

A: The given problem is to prove the following set identity using the contradiction method.

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: Let F be a nonempty family of transitive relations. Prove that intersection F is a transitive…

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Q: Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is…

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Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

Q: Suppose that X is a set and {A. : a E I} is an indexed family of sets (which contains at least one…

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Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: For all (x,y)∈A×A,(x,y) ∈ S if…

A: Solution : Given :             A = {3, 5, 7, 8} ,                         S is a relation from A to…

Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

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Q: Let A = {1,2, 3, 6}. Define a relation R on A as follows: x Ry if y – x > 0 Write out the relation R…

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Q: Let R be the relation on the set of people with doctorates such that (a, b) ER if and only if a was…

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Q: In each item below, verify that ~ is an equivalence relation on the given set. (a) Let S = Z x N.…

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Q: Jive R² which are example of two subsets homeomorphic. not C specify the set explicitly) g

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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: Let Let R be a relation from A to B defined by Then Select one: O a. O b. O d. A = {0, 1, 2, 3, 4}…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: For each of the following relations on a set {1, 2,3,4}, decide whether it is reflexive, whether it…

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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: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: Let X be a set. Show that P(X)÷ X.

A: Solution:Let X ba a set.To Prove: P(X)≠X

Q: Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

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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: 2. Find a set A such that A = {2, JA]}.

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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: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

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