Answer the following questions for the poset ({{1}, {2}, {4}, {1, 2}, {1, 4), (2, 4), (3, 4), (1, 3, 4), (2, 3, 4} }, ≤). Find the minimal elements. (Check all that apply.) (You must provide an answer before moving to the next part.) Check All That Apply {1, 3, 4) {1} {2} {4} (2, 3, 4)

Q: Draw the directed graph of the relation R = {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} X=123 43

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Q: List all the subsets of {x, y, z, y}.

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Q: 2.) Create two sets, A and B such that An B = 0 and A UB= (1,2,3,4).

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Q: Provide a proof of the statement given below the figure. You may submit your proof in any format…

A: ABCD is a kite with  AB≅ AD          and  CB≅ CD We need to prove that : ∠B≅∠D

Q: Help with this please

A: The objective of this question is to prove that for any two bounded nonempty subsets of real…

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Which of the following sets spans Rº 3 None O {(1,2,3),(0,0,0)(-2,1,0)} {(2, – 1,2),(4,1,3),(2,2,1)}…

A: vectors span R3 means that some combination of the vectors can take up all of the space in R3.

Q: Consider the partial order with domain{3,5,6,7,10,14,20,30,60}and with x ≤ y if x evenly divides y.…

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Q: Let 2 = {a, b, c}. Write down all possible o-algebras on N.

A: Given: Ω=a,b,c

Q: List down the elements of A = = {x|x²<45,x € Z} A) {0, 1, 2, 3, 4, 5, 6} B {-6, -5, -4, -3, -2, -1,…

A: The objective is to list down the elements of A.

Q: Let G={1,-1,i,-i} with usual multiplication then G is isomorphic to Select one: a. Z, x Z, b. (Z, +)…

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Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: Given R, = {(1, 2), (2, 3), (3, 4)} R2 = {(1, 1), (1, 2).(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3,…

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Q: Use any method you choose to shc are sets.

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Q: 1. Let X-(a,b,c} and T X={Ø,X,{a},{b},{a,B}}, (i) Write down all open subsets of X. (ii) Write down…

A: If (X,T_X) is a topological space. Then elements of T_X is called open sets and a set is closed if…

Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: This is a question with multiple sub-parts.So I solve only first three parts. Re-post the question…

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B) n (A x C)

A: we have to prove the lemma .

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: 4.) If the Cartesian product of A x B is {(1, 1), (1, 2), (3, 1), (3, 2), (5, 1), (5, 2)), what are…

A: Topic- Cartesian products of sets we are given, A×B={(1,1),(1,2),(3,1),(3,2)(5,1),(5,2)}if…

Q: Express each set below using the roster method. Write all elements in increasing order. Do not…

A: Introduction: In Maths, sets are a collection of well-defined objects or elements. A set is…

Q: How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in…

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Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership tables.

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Q: The set {[1 2 0 1, [2 0 4 1, [O 4 5 ]}spans R3 صواب İhi

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Q: Let ai = [250] -10 and a2 = h [4] The set {a1, a2} will span R² unless h = (If there are no values…

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Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3),(4,5)} on the set A =…

A: Let R be a binary relation on a set A. R is said to be  reflexive if for all . R is said to be…

Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: b) in the answer provided, we see the systems S1 and S3 satisfy the closure property.      For…