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Q: 2rint thedemain and Yange Fanctions 131

A: Domain:it is the set of value of x of a function which will give output y.it is set of possible…

Q: Let the functions 13:R-¬R, with 3 メー X2 Proove that. V(4xs) =3 (Vx{)-4 (Vx)

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Q: Q: Show That Уо ни дуот исто вул - Уе жиду, ти син) ду ?! ?!

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Q: 4 Given fax) = 3 Caloulate flA) with domain (2,'e

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Q: 5- If X, ~B(6,1/3) ,X, ~B(8,1/3), X, ~B(10,1/3) , then Y = E X, ~

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Q: What are the three conditions under which the following is a correct statement: (Ах В) х В- Ах (ВхВ)…

A: According to the given information, it is required to tell the conditions under which the following…

Q: a) (A u B) = A N B b) (ANB) = A u B

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Q: 12) Let X1, X2, X~N(u, 62) which the following statement true a) X-N(,82),S2~x…

A: Step 1:X1​,X2​,..,Xn​∼N(μ,δ2) independentlyThen sample meanXˉ=n∑i=1n​Xi​​We know…

Q: O show that 2. I| a+ V 1= 11 + 1i if and only if ū. ů =0 %3D

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Q: yA B1, 1) R: A(l,0)

A: As per bartleby guidelines, for more than one question first one needs to be solved. The required…

Q: 1 Premises: p → (q ^r), s → r, r → p. Prove: s → q. 2 Premises: -(r v s), ~p → s, p → q. Prove: q.

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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: (9) 1. ~ GƆ (A v B) 2. - B 3. AƆ D 4. - G/;, D

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Q: Let U= {q,r,s,t,v,w,x,y,z}  A={q,s,u,w,y}  B={q,s,y,z} c={v,w,x,y,z}  determine A n B'

A: Given that B={q,s,y,z} So, B'= U - B= {q,r,s,t,v,w,x,y,z}  - {q,s,y,z}= {r,t,v,w,x}

Q: Use the identities A = ANS and S = BUB and a distributive law to prove the following. (a) A = (ANB)…

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Q: a) n(A) =    b) n(A∩B) =  c) n( B' ∩ C' ) =

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Q: (ove) V (IAS) (0~1) V (1~VO)~ (pv~e) ^ (~p^r) :. LAS

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Q: Find ||u||, ||v|l, u.v, and d(u, v). u = (-1, 2), v = (2, 7) (a) |lu|| (b) ||v|| (c) u- v (d) d(u,…

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Q: Which one of the following is the value of r = for f(3) which is obtained from the Newton forward h…

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Q: What is the domain of h? ) (-2-1, 1, 5 and 6) 25x56 D (5-26, and 7)

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Q: find X(Z) if X (K) = (₂₁) K X(Z) = { X(K) Z-k k=0 K=13,5

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Q: Let U{m,n,o,p.q.r,s,t,u,v} and K{k.l.m.n.v). Find the compliment of K (K').

A: We have to write the elements of U which are not in K

Q: Write the following arguments in vertical form and test the validity. 1. ((p → q) ^ (r → s) ^ (p V…

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

Q: 28. Evaluate : a) A (3e) b) Aʼ(ab)

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Q: 03)Find: T(n+1)% = 1) 2) 3) T(e)= %3D

A: 1. From the definition of gamma function we know that τ(n+1) = n!

Q: 4. Prove that (a) A\B=A\(ANB) (b) A\(B\C) = (A\B)U(ANC) (A\B)\C=A\(BUC) (c)

A: To prove the given equality we shall use the following rules 1.   A \ B=A∩Bc 2. De Morgan's Law:…

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>a then it can be written as: x<-a or x>a Now, we have x∈ℝ: x+3+x>2 Now,…

Q: 4 (6) Let U = {a, b, c, d, e, f, g, h } A = {a, f, h } B = {b, c, d, f } C = {b, c, d, e, g } %3D…

A: Given U = a, b, c, d, e, f, g, hA = a, f, hB = b, c, d, fC = b, c, d, e, g

Q: If v = V2 = v3 = and v = a,v1+a2v2 + azV3, then find a2. 4 DA) a2 == O B) a2 a2 . az = O D} n az = O…

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Q: 11. Simplify the following expressions: 11.1 z=¬¬(ave) v (πv¬0)) 11.2 z=(¬α ^ß) v (B^¬μ) V(B^H) Z=

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Q: Prove the following: (A → B) ^ (B → A) (D ∨ E) → B A → (~E ∧ C) ———————— ∴~E

A: We prove the given argument by using rules of inference.

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.