One of the following inegualities holds for every xand y belong to real numbers R. اختر احدى الدجابات

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

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Q: Provide a counterexample for the statement: For any sets A,B and C, А - (В -С) — (А - В) — С.

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Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

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Q: write as interval the set defined on the real line 45 67 8 -3 -2 -1 0 1 2 a) b) -2 c) -5 -4 -3 -2 -1…

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Q: Which of the following set is consistent? Select one: O i. None of these O i. (A&~(BVA)} O i. (/ ) >…

A: Option 4 ) { A ⊃ B , B ⊃ C , A ⊃ C }  is correct

Q: Construct an example of a example of a Tautology not covered herein.

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Q: (BUA)NC

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Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

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Q: 1. A = {2,5 – 7} and B = {a, k, u, j}. What is A x B? 2. U = {11, 22, 33, 44, 55}. V = {1, 2, 3, 4}.…

A: As per guidelines, I can answer only one question.

Q: Let U={-5,-4,-3,-2,-1,0,1,2,3,4,5}, A={0,1,2,3,4,5} and B={-4,-2,0,2,4}. Perform the indicated set…

A: The given sets are U=-5,-4,-3,-2,-1,0,1,2,3,4,5,A=0,1,2,3,4,5,B=-4,-2,0,2,4.

Q: Describe the set of real numbers satisfying Ix - 31 = Ix - 21 + 1 as a half-infinite interval.

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Q: Which x satisfies both Ix - 31 < 2 and Ix - 51 < 1?

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Q: Let S be the set of all real numbers except -1. Define * on S by a*b = a + b + a b. The solution of…

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Q: (d) List all outcomes in the event D that exactly two vehicles go in the same direction. D = (e)…

A: See the handwritten solution

Q: Show each of the following is valid using Rules of Inference and Laws of Equivalence: r v ~p -p = s

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Q: 1. Determine whether the vectes (,2,3), (3,3,1), 3,1,2) in R?. indefendnt are

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Q: Explain the difference between o and oz and between ju and u The quantity u is the -Select- quantity…

A: Introduction: Denote X as the random variable of interest. Suppose a sample of size n is taken from…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: What is the statement x > 15 and x < 17 interval notation? O [15,17] O (15,17] O (15,17) O [15,17)

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Q: A How many paths are there from A to C?

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Q: Using set identities, prove the following. a. AUBUA)=AUB b. A=\AUBUA || с. (А-В)-С-(А-)-В |

A: Here using set identities  De Morgan's law Associative law Complement law .....

Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: Which of the following set is consistent? Select one: O i. None of these O ii. (A&~(BVA) } O i. {J>…

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Q: Let S, be the set of real numbers such that their decimal ex- pansion contains 3 at l-th place after…

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Q: mutually disjoint? Why or why not?

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Q: 4. Let R+ be the set of positive real numbers and N+ be the set of positive natural numbers. Prove…

A: The objective of this question is to prove that for all positive real numbers a and b, and for all…

Q: Exercise 8. [1, 2.2.10] Show that F₂Q1v₂ [c] iff a Vv₂Qcv₂ Here Q is a two-place predicate symbol…

A: Given information:A first-order logic structure denoted as A.Q is a two-argument predicate symbol.c…

Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

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Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

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Q: Which interval notation represents -3 ≤x≤3? 1) [-3,3] 2) (-3,3] 3) [-3,3) (-3,3) 4) 1 O O O O a b n…

A: From the convention of interval notation, We can write: a≤x≤b  as x∈[a,b] which represents x which…

Q: (c) A \ B = A \ (An B). (d) A = (ANB) U (A \ B).

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Q: Write the mathematical formulas corresponding to the following statement with the help of the…

A: Given statement : Every function with positive and negative values has a root.

Q: (FNB) UC'

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Q: Let A, B and C be any three sets. Then Ax (BUC)=

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: Exercise 2.i) (1p) We learned that if E EM then E is nearly a closed set. Write that statement in…

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Q: 4 The set {# € R : \# + 3| + z > 2} equals Select one O a (-0, -3) U|-,00). O b.(-3, 0). O d none of…

A: If we have x&gt;a then it can be written as: x&lt;-a or x&gt;a Now, we have x∈ℝ: x+3+x&gt;2 Now,…