find fundamental set of soleubions cwith d real va lues for

Q: If ftickiieI{ is acollechion of Subsets ofX then く) andh %3D det the equality not (X;)-( true in…

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Q: If geR[a,b] and if hGx) = gCa) except for a finite num ber of points in [a, b], then prove that…

A: Here we apply riemann integration formulas.

Q: Let's compare the cardinalities of N and I.

A: We will find out the required solution.

Q: Let S={xEZ:x+2=6(mod 15)}. Then Sis is the empty set a countable set is an uncountable set

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Q: Queston2 {e-x, xe-O onlo, c∞) a) shau that q fandamented Set

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Q: 1. A is a well defined collection of 2. objects called 3. If A and B are sets, then B C A iff In tho…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=A.

Q: theorem Every Ving Can be imbeobling în aving with

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Q: If lal = n, show that |a'| %3D gcd(n,t)

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Q: ofind all voots ecilmal Places.

A: Use Newton's method to find all roots of the equation correct to 6 decimal places1x=1+x2

Q: (5) If possible, give an example af each af foll o ing la) Sets A,B and c Snch that As B, B$ C A CC.

A: Here we have to solve 5(a) and 5(b) We have to give an example about the given condition.

Q: Prove: Vn, meZ,if n and m are odd, then n-m is even

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Q: If ara Ec (R) for thand R is all a ER en Prove Cmmutafive.

A: Given that   a2+a∈C(R) for all a∈R   Let  a,b ∈ R, such that a2+a=0 and b2+b=0…

Q: If geR[a,b] and if ha) = g(4) except for a finite num ber of paints in [a,6], then prove that…

A: Given:          g ∈ R[a, b] and h(x) = g(x) except for a finite number of points in [a,b] To…

Q: (i) (Z- Q) and specified in it using the most concise notati

A: Firstly we write elements of both sets Z and Q and then find Z–Q

Q: Prove that cot7+ cot8+ cot18 = cot3 %3D

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Q: Jin Let G beagreupsuch that I6tefs thens

A: Answer

Q: (2) (a) Show using set identities that AUBU (AOBOT) = AUBUT (b) Prove by contradiction that if A C…

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Q: The number of non-empty subsets of B is |{S:SC A, S = 3 and Sn B = 0}| = max {|S|: SC AUB, SNA| is…

A: Given that A and B are finite sets satisfying A=6, B=7, A∩B=2. Since, B=7. So, total number of…

Q: Let D be digraph. If id(x) > 0 for all x ∈ V (D), then D contains a circuit.

A: Given:- Let D be digraph. If id(x) > 0 for all x ∈ V (D)

Q: 2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

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Q: (1) Let A and B be sets prove the following. (b) ACB if and only if An B = A. %3D

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Q: yoint each. On the Cverage. Une jaint defectuve to be free from i How moy defective joints in a gets…

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Q: Prove: Vn,meZ, if n and m are odd, then n-m is odd.

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Q: şa,6şc2.Debine a selation I on. pl2) which satisfies. For all set A and B in P(X) AJB ANB+

A: Given x={a, b, c}P(x)={ {a} , {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}, ∅}a relation onJ: P(x)…

Q: One of the following statements is true: A) Archimedean property say that if y > 0, x € R, then…

A: Archimedean property named after the mathematician Archimedes. The set of real numbers ℝ has the…

Q: How many funcei ons F{,2,3,4is}→ {l,2,3} are ehere eien er FCI)=1, F(2) 2, f (3) =3? or

A: To find the number of function f such that either f(1)=1 ,f(2)=2 or f(3)=3 .

Q: 2) het A, B and non- dijoint diagranı be Three Cveyla Ony using sets von Show (B-C)Ule- A) # A-8

A: firstly, we will draw all given set region then we comparing both side

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

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Q: Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A: To prove A∪B∩B∪Ac=B If A and B both are empty sets φ, then there is nothing to prove. If A=φ, B≠φ,…

Q: (3) Let S = {; Find with prove :m eN,n E N}. %3D suprenum of S. (4) What is an unbounded set?

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Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

Q: Which postulate or theorem should be used to prove AHIG AJKI? G O ASA O SAS O SSS O AAS

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Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: Let S={xEZx+2=6(mod 15)}. Then S is* is the empty set a countable set is an uncountable set

A: A countable set is either finite or denumerable. Given: S=x∈Z:x+2≡6mod 15

Q: 4 in [2, 4] sat theorem, ther

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Q: Prove by unduclion Hhat if ne IN - 31,2,3,...f aud 9> 2

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Q: Let A1, A2, ... , An be any n sets, n 2 1. Show that (U-1 Ar) = U=1 Ar %3D

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Q: Let A = {a, a, b, c} and B = {a, b, c}. Prove that A = B. Thus, the number of times an element is…

A: Given A={a,a,b,c} and B={a,b,c} we  have to show that A=B, for  this we will show that A⊂B and B⊂A…

Q: Let X + 0, |X|> 2. Then (X, Tna) is not To -space. Select one: True O False

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Q: If i and i are in R™, then –i is in span {ū, 3}. |

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Q: prove that (1, 6) 13 an o pen set 13 an open çet.

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Q: Show that if A and B sets then A – B = ANB

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Q: Prove that Yational numbers la b) with equality multiplication and addition defined as Set s of…

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Q: Find elements o and t in S3 such that lo|=2, IT|=2 and lot|= 3. How many elements in S4 are there…

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Q: Prove (((LOM)-N) U(N-(LUM))) < (LU (MUN)) L, M, N are sets.

A: To prove: L∩M-N∪N-L∪M⊂L∪M∪N

Q: Let S={xEZx+3=4(mod 20)}. Then S is a countable set is the empty set is an uncountable set

A: See solution below

Q: Let X = {a, b, c} and R={(c, b),(a, c)}. Then Check the all properties reflexive,symmetric,…

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Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .