Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

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Q: to,' i.e. Let X be the space of integers and let R be relation 'less than or equal x Ry if x ≤ y…

A: The given relation is .

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: Prove that for any sets A, B, X - X − (An B) = (X − A) U (X – B). -

A: .

Q: 14. How many one-to-one functions are there from a set with five elements to sets with the following…

A: In this question, we have to find number of one-to-one functions formed between two elements.…

Q: Let A = {1, 2, 3, 4, 6}. Let R be therelation on A defined by {(a, b): a , b ∈A, b is exactly…

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Q: 2) Define a relation R from {a, b, c} to {u, v} as follows: R = {(a, v),(b, u),(b, v),(c, u)}. a)…

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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: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Suppose S is a nonvoid, bounded set of real numbers. Let - S denote the set {-x: ES}. Then inf(S)…

A: The answer provided below has been developed in a clear step by step manner

Q: A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B)…

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Q: Suppose A and B are nonvoid, bounded, disjoint subsets of R. Mark all of the properties that must be…

A: A and B are nonempty bounded disjoint subset of ℝ

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: If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret…

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Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: 5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that…

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Q: Find an orthogonal set with the same span (and same number of elements) as [2] [8]} (18118)} "

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Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

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.