(c) A line in R² not through the origin ax then ŏ ¢ H. : Itis not asubspace Umecepsung but ealightenng i You could wri'te this as a Gob set, H, of Re Hie Is H closed under ☺ ļ Is H closed under ☺ ļ

Q: Let a1 = ht 11 and a2 = h [40]. . For what value(s) of h will the set {a1, a2} span R²?

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: . If A and B are sets in a universal set U, then AUB=AnB.

A: We proved this by wave diagram

Q: Prove the following statements if they are true and give a counter-example if they are false. a) For…

A:

Q: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

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Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: Please refer to the solution in next step.

Q: 12. Statement 1: All X are Y Statement 2: All Z are X Statement 3: Therefore, A. all Z are Y B. some…

A: Statement 1:All X are YStatement 2:All Z are XStatement 3: therefore=?

Q: otic 6) Use Classral Version step by skep tndhuding the flue es finds of f='Caiy, 2) thre shetch the…

A: We have to find the flux ∫∫σF→.n^ dS, of the function F→ = <x, y, z>, over the surface σ: z =…

Q: . If A and B are sets in a universal set U, then AUB=AnB. A-(BnC)=(A-B)U(A-C). . If A, B and C are…

A:

Q: Give ane example of each of the tollowng. Also justif your choice of exxample (i) A self adgoint…

A:

Q: Let A, B, and C be sets. 1. Prove: If A C B then ANC C BnC. 2. Disprove: If AnC CBNC, then A C B. 3.…

A:

Q: Exercises for Sets and Functions Q1) How many elements does each of these sets have? b. P(Ø, {Ø),{Ø,…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: Which of the following statements are true for all sets A, B, and C?

A:

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: 1. Complete each statement for the translation T:(x, y) → (x + 3, y - 1). a. T glides points units…

A: T:(x,y)→(x+3 , y-1)

Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: 15. If A, B and C are sets, then (AnB)-C=(A-C)n(B-C). m

A:

Q: 2. Suppene F=Q . L the set 4 2 3 4 lnianly ? why any o? nhar happeno is F=Zs ? nidependent so? rhar

A:

Q: Find, the domain of each of these, ped pred cates where the doman is the set of untegers లు రుంకు

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

Q: 48. Let A, = {...,-2, –1,0, 1, ...,i). Find %3D a) Aj. b)4-

A: The meaning of the set  ∪i=1n Si where S1,S2,……,Sn are the sets . The set ∪i=1n Si is collection of…

Q: f. Connider the ret { KI, E, P, 21 , Q ,Q°, R*, R, C }, integers, P Q w the whee E i the set all…

A: Please check the answer in next step

Q: TOVE 4.55. Let A, B and C be sets. Prove that (A-B) (A-C)=A-(BUC).

A:

Q: acks. set R A Lanchtwely then slow that sestintionof the action of an not by the on. Fuslid, then…

A:

Q: |somotphic (Similar) orderede sets: suppose x anel y are partially ordered set ,and fixay…

A: We have to give the example of the isomorphic ordered set.

Q: Proposition 1.35. The intersection of any family of closed sets in a metric space X is also closed…

A:

Q: lve an example to Show "arbi ombitrany union of again open s tue result: true open sets is for…

A:

Q: O -L -5) O4-

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Q: Question 2 Given is set A = {1,2,3,4}and relation RCAXA, define on the picture 2 This realation is:…

A:

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: Let A = (-2, 4)., and B = [0, 0). Choose sets that are infinite and uncountable. O B° \ A O Bº nQ O…

A:

Q: if Re (a) a/b and ble a 13 divi on R i called transitive. (b) a/b as a/c = a//b+c)

A: Given : If R is a commutative ring, thenClaim :             (a) a∣b and b∣c⇒a∣c i.e., this relation…

Q: 18. There is a set X for which Ne X and NsX.

A: As N is set of natural numbers , so  for N to be subset of X and N belongs to X , we can consider X…

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: To prove the equality A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that each set is a subset of…

Q: 17. If A,B and C are sets, then Ax (BnC) = (A x B) n(A x C).

A:

Q: 18. If A,B and C are sets, then Ax (B-C)= (A x B)-(AXC).

A: By the using of definition we prove this.

Q: H.W let f:AC, 9: B D be two fanctin. sit flx)= 96 VxE AAB hz fug: AUB CUD defied by s then XEA g),…

A:

Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C),…

A: SOLUTION-

Q: Q7 IF THE MAPPING BETWE EN I AND ã is: WHERE A 1s A 2x2 MATCIX OF CONSTA TS., AND T a) GHOW 2

A:

Q: 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C).

A: To prove the equality (A∪B)-C = (A-C)∪(B-C), we need to show that any element x belongs to the…