Define the sets A, B, C, D, and E as follows: • A = {x €R:x<-2} • B = {x €R:x> 2} ' = {x € R: |x| < 2} • C = Do the sets A, B, and C form a partition of R? If not, which condition of a partition is not satisfied?

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: For the given set A, determine whether P is a partition of A. A = R ("All Real Numbers"), P =…

A: Here, A= R ("All Real Numbers") P={C" sub "y: y is an element of R and y &gt; 0}, where C" sub "y =…

Q: Let A be an m x n matrix, and let B and C have sizes for which the indicated sums and products are…

A: If the product AB is defined, the entry in row i and column j of AB is the sum of the products of…

Q: A partition of a set has four subsets: M, A, T, and H.  If P[M] = 0.143, P[A] = 0.378, P[T] = 0.278,…

A: We want to find P[H].

Q: (a) Determine whether or not it is convex or concave. A = {(x, y) = R²|yx4, and -2≤ x ≤ 2} B = {(x,…

A: Necessary Sufficient Nature f'x0=0 f'x0=f''x0=f'''x0=..=fn-1x0=0  fnx0&gt;0 n even Convex f'x0=0…

Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

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Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

Q: Given sets X, Y and Z, use the set properties to show that (Z – X) n (Z - Y) = Z (XU Y), indicate…

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Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: Find the indicated sets. (a) P({1,2} × {3}). (b) P({1,2}) × P({3}). (c) {X e P({1,2,3}) : 2 EX}.

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Q: Give the relation R induced by the partition above on A.

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Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

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Q: graph the complement of the following set S={ (x,y) l 2x+3y>=12

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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: 4. Describe the image of the following sets under the following maps (a) f(2)= for S S = {0}; (b)…

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Q: Classify each of the following as either Discrete, Continuous, or neither Discrete nor Continuous:…

A: The objective of the study is to identify the data type for the given statement.   From the known…

Q: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: A Partition of a set has 3 subsets: A, B, and C. If Pr[A]=.25 and Pr[B]=.45, find Pr[C].

A: The provided information is,P(A) = 0.25P(B) = 0.45According to the general law of probability, the…

Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  &amp; T=0, 2, 4.

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: Pick a subset from R and call it X. Let your mark on this final examination be x, prior to any bonus…

A: Question: Pick a subset from R and call it X. Let your mark on this final examination be x, prior to…

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…

Q: 3. Determine if the set Q n (0,1) is open, closed or neither. What is the boundary of the set? Also…

A: 1. Q ∩ (0,1) is neither open nor closed. 2. For the set Q ∩ (0,1), the boundary includes the points…

Q: prove: for any two sets X and Y, #(X x Y) = #(X) • #(Y)

A: To prove it equals the product of the cardinality of both the sets.