Exercise 1.2.5 (De Morgan's Laws). Let A and B be subsets of R. X (a) If x = (An B)e, explain why x A UBc. This shows that (An B) C AC U Bc.

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Q: 10 -8 -2 -2 0 2 2 -2 24. Let A = and w = Determine 1 -1 1 0 -2 if w is in Col A. Is w in Nul A? 6

A: Consider , A=10-8-2-2022-21-160110-2  and w=2202 To determine if w is in column of A. In matrix take…

Q: Question 1 Prove that the number of pairs (A, B) such that A C B C {1,2.n} is 3".

A: Let the set A is containing n elements then number of ways to pick r elements out of n elements is…

Q: A is symmetric

A: In this question, we have to check the matrix A is symmetric or not.

Q: QUESTION 6 Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False. QUESTION 7

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Q: Let A = 4a, + 2a, - a and B a and B = aa + Ba, +3a₂ (a) If A and B are parallel, find a and B (b) If…

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Q: Anikwenie 46. If P(A) = 0.5, P(B) = 0.40 and P(A U B) = 0.70, find P(A/B) and P(A U B) where A is…

A: Given that P(A) = 0.5 P(B) = 0.40 P(A U B) = 0.70

Q: Let o+ a eR and let G= {na| nez} ,then (G, +) is an abetian gronp. ( Hint: the identity element is…

A: Let 0≠a∈R and let G=na|n∈Z, then G, + is a group if the following properties are satisfied. 1.…

Q: (а b)с + (а - с)b + (с b)a 3 ve that v belongs to B.

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Q: If A and B are independent, and the P(A) = 0.35 and P(B) = 0.45 find: a) P(A ∩ B)…

A: Given that P(A) = 0.35 P(B) = 0.45 A, B are independent events.

Q: 1. Solve the following problems below: let U = {a, b, c, d, e, f, g, h, k} A = {a, b, c, g} B = {d,…

A: We have given that  let U= {a, b, c, d, e, f, g, h, k} A = {a, b, c, g} B = {d, e, f, g} C = {a, c,…

Q: Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} α1. Find…

A: Since you have given two different questions therefore we will solve the first for you. IF you want…

Q: If A = {2,3} and B = {x|x EZ, x<3}, then A x B = Select one: O a. {(1,2), (1, 3), (2, 2), (2,3)} O…

A: If A=2, 3 and B=x x∈Z+, x&lt;3, then to determine A×B.

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: Prove that if CE AB and C+ A, then AB AĆ.

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Q: If u = 7 then uu? and u'u =

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Q: Let ā = (1, 5) and 6 = (3,0). Find —ã – b. - - V Λ

A: Answer: &lt;-4,-5&gt;Explanation:For any query with the solution please ask in the comment box.

Q: Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

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Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: If X = {1,2.3}, A and B are IFSs where A= (x,{1},{2}) and B = (x,0,{2,3)) then An B

A: Intersection of Two Sets The intersection of two sets is the set of elements that are common to…

Q: State which of the following statements, are true, vacuously true, or false. (a) If A CAN B, then…

A: I have given the answer in the next step. Hope you understand that

Q: Let A = ff, I, y }, B = {r, a, t}. Find A x B and B X A. AxB= qafhbuifsfvggbh

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Q: Which of the following are always true, and which are not alwaystrue? Give reasons for your answers.…

A: Given statement is u×(v+w)=u×v+v×w

Q: Let {A :A E A} be a family of subsets of IR. Show that • When A is finite, we have

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Q: Q.1) Evaluate IT ycos(ry) dzdy 0.

A: We will find the double integral as following.

Q: [1 2 0] Let A = 1 2 0 0 1 0 and v = Select the statement that is correct. O v is an element of Col…

A: We have to find correct statement

Q: Let G = Z¬ÐU(5). The identity of G is O 7 O 28 35 O 12 O 5

A: We know that U(5) is isomorphic to Z4.

Q: Ex:Let (Q,0)be a slouP. A nodremp ty set HS Q - is a Sab sYou? of G if and on ly if ab" E He fer anS…

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Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

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Q: 1. A service station has both self-service and full-service islands. On each island, there is a…

A: Note: "Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: s) Let ICS(P), 4,0, € S(P), and let I (p = 0). (a) Show that then riff I and (b) r, iff r, 0.

A: As per the question, we have to prove two statements related to the consistency of deductive…

Q: Prove the following statement: (VxR) (x 0 ⇒ (y R) (xy = 1))

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Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

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Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: A = 2 1 2 0 1 -H B = W = w-B Find the following: a- A², AB, det(A) b- If AW=B, find (W) using…

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Q: Y D Prox

A: Product of two sets

Q: (3) (i) Determine the number of positive solutions of the equation x1+x2+x3+X4 = 14, where each x;…

A: Thank you for your question!! But according to the guidelines I will be answering one question only.…

Q: Let {A :A E A} be a family of subsets of IR. Show that • When A is finite, we have U A CU A, N 4…

A: To prove the given statement we need to use the following definition, Union of sets: The union of…