Let U= {x|x EN and x<7) A = {x|x is an even natural number and x<7} B=(x|x is an odd natural number and x <7} C=(x|x E N and 1

Q: Ix-51>7* O x>7, x 12, x 12 No Solotion

A: We have to solve the inequality

Q: Consider the statement Vxy (y <x) Let x be all natural numbers Let y = x-1 Is the statement true or…

A: We know that the set of natural numbers starts from 1 and it is an infinite set. This set is…

Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

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Q: Define two relations R1 and R2 on set positive integers. R, = {(a,b)|a > b} and R2= {(a,b)|a? = b }.…

A: Composition of relation

Q: . Show that if P(A) > 0, then P(AB|A) ≥ P(AB|A U B)

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Q: 16-(4+r) lim is O a. -8 O b. 8 C. 0 O d.4 O O O

A: This is a limit based question

Q: 1. Let X be the set of real numbers with the usual pseudometric. Find the derived set and the…

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Q: Which set consists the possible rational roots of x + 4x - 2x +8 0? A 11, 18 B. 11, 12, 14 C. 11,…

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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: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: Let à =. Find |ā|.

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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: a. 2 |x – 4|| х-1 b. x? + 2х — 12 1 х+1

A: a.  (1, 2] and [3, (5+√17)/2]         b.  (-1-√13 , -1+√13)

Q: Define two relations R, and R2 on set positive integers. R1 = {(a,b) | a > b} and R2= {(a,b)| a² = b…

A: Given that two relations R1 and R2 on the set of positive integers.                    R1=(a,b) |…

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: The set of all real numbers x for which x24x+2+x>0 is

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: 5. Let x and y be irrational numbers such that x-y is also irrational. Define sets A and B by A = {x…

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Q: Proof the following statement in detail: ". Let x ∈ R. Prove that if 3x4 + 1 ≤ x7 + x3, then x >…

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Q: 1. Show that if P(A) > 0, then P(AB|A) > P(AB|AUB)

A: Show that if P(A) &gt; 0 thenP(AB|A) &gt; P(AB|AUB)

Q: Prove the following set identities: (a) (AUB) nC = (ANC) U (BNC); (b) (AUB)-C=(A-C) U (B-C); (c)…

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Q: . Let f= {(-4,4), (-2, 4), (1, 3), (3, 5), (4, 6)} and g= {(-4, 2), (-2, 1), (0, 2), (1, 2), (2, 2),…

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Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 8. For any sets A, B,…

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Q: Let Q be the set of rational numbers and R be the set of real numbers, A = {x e R: 5<x< 10}, B = {x…

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Q: Let T= {Rational Numbers} Q = {Irrational Numbers} E = {Even numbers}               D = {Odd…

A: 1. FALSE

Q: The values of x satis fied a+5| <0, is R {-5} {0} (-5, 5)

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Q: (Væ)(3y)(x² + y = 0) (3x)(Vy)(x2 + y = 0) (3æ)(3y)(x2 + y = 0)

A: