28. Let R be a collection of sets defined by R = {x | x ¢ x}. %3D (a) Show R is not the empty set. (b) Is R an element of itself?

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

Q: For the subset "The set of points on the line given by x+2y=0" verify whether it is a sub space of…

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Q: Let the relation M defined as M={(x,y)|y = /x²-49 a. Write the domain and range of M. b. Is M a…

A: We have to answer all the questions.

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

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Q: Let A be a set and let ƒ : A → B be a surjective function. Prove that there exists a subset CCA such…

A: Given: A be a set and f:A→B is a surjective function. To prove: There exists a subset C⊂A such that…

Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: Draw the relation

A: Given: x,y/x2+y2≤1 To draw: The relation.

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: You are given two graphs G and H with V(G) = {a, b, c, d} and V(H) = {1, 2, 3}. 1. How many…

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Q: Sketch the set M defined by M = {z € C | Re(z²) 1}.

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Q: Let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;…

A: given let ‘E’ &amp; ‘F’ are any two non-empty sets and there order are as follows;…

Q: 4) Let a < b be real numbers. Prove that the half open/half closed interval (a, b) is both an Fo and…

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Q: Q1. Find the image of the set A= [-2 under function sin x.

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Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: A relation R is defined on the A={1,2,3...9.10}  as follows: xRy means "3x- 2y=1"   List the…

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Q: 8. Let A = {1,2} and B = {a, b, c}. For each of the following cases, decide whether the set…

A: The set A={1,2}, B=a,b,c &amp; f:A→B. a) 1,a,2,b b) 1,b,2,b c) 1,a,1,b,2,c

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Let the domain of x and y be all people. Let W(x): "x is a woman", M(y): "y is a man", and Lex.y):…

A: The objective is explain the meaning of the statement ∀x∀y Wx∧My→Lx,y

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: (15 pts) List the triples in the relation {(a, b, c) a, b, c are integers such that 0 < a <b<c<6 and…

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Q: 2. Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: Answer given below.

Q: Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference. It…

A: Unity: Let R, +, ∘ be a ring. If the semi-group R, ∘ has identity element then it is called as unity…

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

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Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

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Q: Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.

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Q: Consider the subset R = R × R − {(x, x)|x ∈ R}. What familiar relation on R is this? Explain.

A: Concept used: Subset relation Subset relations are used to define partial orderings on sets. A set's…

Q: Choose the correct option. The number of onto function from the set {1,2,….,11} to the set…

A: Let the set A be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and the set B be {1, 2, 3, 4, 5, 6, 7, 8, 9,…

Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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