4 Show that a + B = B +a for all a, BE C.

Q: Show that if a|b then -a|b.

A:

Q: Show that: If |z| = 1, then: z' + 4z + 5 z2 + 5z + 6

A: Given: z=1 Then show that: z3+4z+5z2+5z+6≤5

Q: In(z,) – In(-V3 – 1) = -In(2) – 1

A: given the argument ∅ of the complex number -3-i as -5π6.and also the modulus of a complex number say…

Q: how many intergers solutions to x1 + x2 + x3 + x4 = 29 are there for which x1 ≥ 5, x2 ≥ 2, x3 ≥ 6…

A: The given equation is -  x1 + x2 + x3 + x4 = 29 where x1 ≥ 5, x2 ≥ 2, x3 ≥ 6 and x4 ≥ 5 We have to…

Q: Let 21 = 2+ j3 and z 4 j5. Evaluate

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Q: b) Show that XNOT =

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Q: Proved Ax (BNC) = (AX B)n (AXC) %3D

A:

Q: 2. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1 + an-2 + 5, express a, in terms of n.

A: Introduction: The disparities between every two successive terms in an arithmetic progression (AP)…

Q: 5. Prove that (Z, × Z6)/((2,3)) S Z12.

A:

Q: Prove that S3 = Inn(S3) = Aut(S3).

A:

Q: (a,b) is measurable.

A: (a,b) is an open interval.  Open intervals are measurable.

Q: It x~N(μ,σ"), then ²~. Option 2 ption 1 *** *** *** N(0, 1) G(1⁄2,2) x² (2)

A: Given, if x~Nμ,σ2 Then x-μσ2

Q: 2. Show that cÃ=cA.

A:

Q: Prove that S4 = ((1 2 3 4) , (1 2 4 3) ). %3D

A: As you asked for question number 8 , and hence here it is.

Q: Prove that in Q(/-5) we have (3,1+ 2v-5)(3, 1 – 2-5) = (3).

A: To show the equality, first we take an element of the product and show that it is in (3) and then we…

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: 2. Show that div r = 3 %3D

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Q: 81/ show that *if ve(Xジーズ) oif v=(

A:

Q: Prove that √1+i√3+√1-i√3 = √6

A:

Q: A survey of farmers showed that of the farmers, 126 grew only wheat, 111 grew only corn, 93 grew…

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: Show that 1/3  Tn +  2/3 Mn  = S 2n

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Q: Prove that R(5, 5) < 50.

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Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

A:

Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Compute [GL2 (R): SL₂(R)].

A: To find: The value of GL2ℝ : SL2ℝ .

Q: find A1 ∩B1 , GIVEN THAT                                             U= {x ∈ z/ - 7}    A= {x ∈ Z+…

A:

Q: (a, b) is measurable.

A: The answer is given as follows :

Q: 4. Prove that, VR, -11-

A:

Q: Let D = {2, 4, 8) "For every z D, 2x¹ €

A: Given that set D = { 2, 4, 8}  And statement is  " For every x in D,   2| x". We need to check that…

Q: If A ⊂ B, can A and B be independent under any circumstances? Explain

A:

Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: If In a + In(z-7) = In(4x), then z = 11 %3D

A: Since you have posted more than one question we solved the first one for you. For the remaining…

Q: ,- ). Show that there a 3,4

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Q: Suppose gcd(a, n) = 1. Then a(") = 1 (n

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Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

A:

Q: 6. Show directly that inf(B) = 1 for B {N =: 4+1} -

A: The given expression is,  B = {1+1/n : n belong to N}

Q: 5. Demonstrate that Im(iz) = Re(z).

A: It is required to demonstrate the problem 5. Problem 5 is solved below in detail.

Q: 10. Show that F; := 2²' + 1 is composite via Pepin's Test.

A: ......(1) Here we are given the 7th Fermat number. We need to show that, 3F7-12≢-1(mod F7)

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: i prov

A: Given, -a+b It is proved using axioms of real numbers.

Q: 3. prove that: det (AB) det (A) det (B) If A -(:), = - ( :) B = 7 2

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Q: Prove that √2+√5 is irritational

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Q: 3. Prove that (An B)² C A x B.

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Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.