2.6 Using the Venn diagram to prove that (x1 + x2 + x3) • (x1 + x2 + x3) = x1 + x2

Q: 1. Prove that 7(x – 1) 2.

A: Let, f(x)= ex-7x+7 ,for x≥2. Differentiating both sides with respect to x, f'(x)= ex-7≥0 . This…

Q: Prove thq+ for all integer a, b, and c if 9+b of a and k is even.

A: Introduction: Even and odd numbers are also referred to as: Even Number: An even number is one that…

Q: Find the least integer n such that (2x^3+x^2logx) is O(x^n).

A: The given expression is 2x3+x2logx. Concept used: Let f and g from the set of integers or the set of…

Q: Prove the following by contrapositive: If x is an even integer, then x² is even.

A: Let x is not even, it has to prove that x is not an integer or x2 is not even. Let x is not even…

Q: Represent in the Argand Diagram all such z for which |z+ 12 - 5i| < 6

A:

Q: 1- - If イ -1 provethat Kt K_9I

A: We have given that a matrix k of order 3*3.

Q: Prove that the K4 is not consecutive.

A:

Q: Find a counterexample to Lie's Theorem when k is not algebraically closed and chark = 0. %3D

A: According to Lie's theorem, for any finite-dimensional linear representation of a finite-dimensional…

Q: (b) Prove that xe" 2 for some x in (0, 1). %3D

A: By the intermediate value property of continuous function if a function f:(a, b) --&gt; R be a…

Q: 4. Show that in the following sense: for any ɛ > 0, there exists Ro >0 so that for any R> Ro, R rp

A:

Q: Suppose x and y are any integers. Prove that if x and y are odd, then x + 5y is even

A: Suppose x and y are odd integers. To show x+5y2 is even. Note: Square of an odd number is odd.…

Q: () is even. 3. Prove that for all positive integers n, the number

A:

Q: 2. Prove that L(cashkt)= ki 52-K2

A: To prove that  L(cosh(kt))=ss2-k2

Q: Find an expression for sup in terms of inf E, sup E, inf F, sup F and prove it. 2F

A:

Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y&gt;9⇒x&gt;54∨y&gt;49, where x, y∈ℝ. Prove the statement using method of…

Q: is the gropt Q whch of Hhe of followring

A: Given that: 1. y=x2ex2. Graph of f(x)

Q: Find a number t such that In(4t + 3) = 5 %3D

A:

Q: Find k such that, 2 det 4 li0 -8 -5] -1 -7 = 510 k 0 .

A: Given det2-8-54-1-710k0 =510 we have to find k

Q: Prove that gcd(a, b) is the least natural number representable in the form ax + by with x, y ∈ Z.

A: We have to show that gcd(a, b) is the least natural number representable in the form ax + by with x,…

Q: 2 5= {(0, 0₂, 93) | DER₁, A₂ER₂, az ER₂ Z Show that sis subring of RxP₂Rz

A: We have to show that S is a subring of ring R1×R2×R3.

Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

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Q: PROVE that 2a + b = 0.

A:

Q: prove for any 2 non negative integers x and y, where x>y, if their gcd IS Y, THEN THEIR LCM is x

A: The objective is to show that LCM(x,y)=x, given GCD(x,y)=y; where x and y are non-negative integers…

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

Q: Is z(√2) isomorphic to z(√3)?

A:

Q: 10. Prove that Z has no smallest element.

A: we will prove it by contradiction, Suppose x belongs to Z  is the smallest element.

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

A:

Q: Prove directly from the definitions that for all integers m and n, if m and n have the same parity,…

A:

Q: Suppose that k and n > k are fixed positive integers. Justify the identity k+1,

A: Given k and n≥k are fixed positive integers.

Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: Show that th equation x" + y² = z" (mod 5) has nonzero solutions in Zz if and only if n is odd.

A: Given: xn+y2n≡zn(mod 5)

Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1- 9/if it of Prove that yś(-)- TT

A: In the question it is asked to prove y'(0)=π for the given function y=2xcos-1(2x)-1-4x2.

Q: (2) Let f(x) = cos (2x). Find the Hermite interpolation H3(x) using xo = 0 and x1 = , and use error…

A: Given: fx=14cos2x We have to find the Hermite interpolation H3x using x0=0,x1=π4…

Q: Prove that Z Q has the universal property of inverting non-zero elements.

A: in Mathematics, Z is the set of Integers. and Q is the set of all rational numbers. Z→Q Let f(α)=1α…

Q: 3. Prove that eª >1+x for x > -1

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Q: Prove or disprove: If xn ≥ 0 for all n ∈ N and lim sup xn = 0, then xn → 0

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Q: coth- x = In () Q1/ Prove that

A: To prove coth-1x=(1/2)ln[(x+1)/(x-1)]

Q: 2. Suppose that {v1,... , Vp} is an orthonormal set in R", and that x E R". What can you say about…

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Q: Prove that the number V7 lies between 1 and 2.

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Q: Prove that ifx^2−6x+ 3is odd, then x is even

A:

Q: Show that on finite m

A: To prove that on finite measure, Lpand almost everywhere convergence are independent.

Q: Suppose x and y are any integers. Prove that if x and y are odd, then x + 5y? is odd.

A: We have to solve given problem:

Q: 2) Show that g(x) = 215 x* + 623 x3 - 37 x2 + 111 x- 15 is irreducible over %3D Q.

A:

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

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Q: 2. Show directly that sup(4) = 1 for A = {1- : n eN}.

A: As we know that, 1&gt;1-1n ∀ n∈ℕ Therefore 1 is the upper bound of the set 1-1n:n∈ℕ. And for each…