Let A(x) be an open sentence with variable x. Show that the converse of (∃! x) A(x) ⇒ (∃ x) A(x)  Is false.

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: 7 Evaluate using Convolution theorem: L-¹{²(²+4)} 2

A:

Q: 9. Show using the definition of big 2 that x² + 2x-4 is 2(x2). Find values for C and k from the…

A: Using the definition these symbols we can reach to answer.  K=1 C=2

Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

A:

Q: Augustus de Morgan satisfied his own problem: I turn(ed) x years of age in the year x2. (a) Given…

A: Augustus de Morgan turned x years in the year x2 and he died in 1871 so…

Q: if f(x1,x2) = e-*-*2, 0 < x1 < o, 0 < x2 < o, F(x1, x2) = e-Xie-x2 + e-X2 True False

A:

Q: How can I show that f(x) is O(x2), where f(x) = 6x2 + x + 1

A: Given: f(x) = 6x2 + x + 1

Q: Ive for æ if In(x? – 1) = 0.

A:

Q: Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂…

A: 1.   0 ∈ ∅ As ∅ is empty set so it can't contain any element. Hence 0 can belongs to ∅. Answer:…

Q: Let f(2) = In[="(= + 7)*(z² + 7)°] f'(x) =

A: Given : fx = lnx8x+72x2+76

Q: Prove that for x≠0 the inequality ex&gt;1+x holds.

A:

Q: A factory received a shipment of 11 lightbulbs, and the vendor who sold the items knows there are 3…

A: Given in the question: Total bulbs, N = 11 Defective bulbs, x = 3 Now we will calculate the sample…

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: 5. Prove that if X, 4 X and Y,n 4Y, then X, + Y, 4 X + Y. Hint: Use an argument similar to the…

A:

Q: EX/ Dis cusse The nature of the Serief 12+4-8+16 –32 +---

A:

Q: Suppose that .3 f(3) = }, and f(x) > 0, and juw <0. < 0. Is it possible that f(2) = . %3D False O…

A: You have asked two different questions. As per the company guidelines we are supposed to solve first…

Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

A:

Q: الواجُب (x-1) (x+4)<o 2 )و - رصه - (

A:

Q: If X~ GAM(1,2) then Var(X)= (1 4 (2

A: Suppose X is a random variable having gamma distribution and X~GAM(α,β).Then, Mean E(X)=αβ and…

Q: A conjecture has been proven true using mathematical rules. O True O False

A: Given query is to find the statement true or false.

Q: determine derivitive c(x)=ecos(x^2+1)

A:

Q: 4. Find all values of x satisfying In[(2x + 1)(x +2)] = 2 In(x+2). Verify the values of x you found…

A:

Q: 1. Use double inequalities to show that: |1 6 3* -5 1 3 then xe -86 941 8. i) if 8 礼1 then xe (3 –…

A:

Q: 3 If ƒ (x) = 2 + x, evaluate Σƒ (k+1). k=1

A: We can answer the question as below.

Q: If X~ GAM(1,2) then Var(X)= 4 (1

A: We have to solve given problem:

Q: If E(X) =1 and Var(X)=5 find E[(2+X)2] Var(4+7X)

A:

Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: -a = Y express L and K as expressions of

A:

Q: Please help me if these 2 statements are right.

A: Statement 1 is false Become for x= 0 there are two values of your.  I. e. There are two image of x=…

Q: What is/are X-value(s) in ex2-3x+2)= 1? 1 (2,1) none of these O O

A:

Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: If 2x³-4x² + x + 1 = 0 so x = 4x² - 2x³ - 1 then x5-x4|<e, X4 = 1.36603, x5 = 1.366024, is the error…

A: Given x4 = 1.36603x5 = 1.366024

Q: The domain of f(x) = Vx2 – 3 is {x:x s-V3 or x2 V3} | True False O O

A:

Q: Show that E( X - K )2 = var( X) + [E(X) - K]2

A: var(X)=E(X2)-E(X)2 E(a)=a  where a is constant (a-b)2=a2-2ab+b2

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: In = In 2. | -2 -2

A: To determine whether the given statement is true or not. ∫−241xdx=lnx−24=ln2

Q: d the sum of the critical numbers of f(x) = 3x4-4x3 +2. %3D ISwer.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let X~N(3,0²). Suppose that P(3<X<6)=0.4 · find P(X<0) ?

A: Given: X~N3, σ2 and P3&lt;X&lt;6=0.4.

Q: Q2-Prove tut- va" - r* ify =()()+ ()F-7 if y =

A:

Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

A:

Q: 6 Evaluate f S Suh

A:

Q: 2. Calcula con precisión n = 2 %3D x2 - 4x + 3.99999 = 0

A:

Q: If P(x)=0, this means that A. The event X might occur. B. The event X will occur C. The event X will…

A: It is given that P(x) =0.

Q: arithmetic without introducing inconsistencies. Explain the reasoning leading to Wallis's…

A: Given: The laws of arithmetic for negative numbers ensure that arithmetic reflects the common-sense…

Q: 3 Prove that Var(aX– b) = a² Var(X) where a and b are constants. %3D |

A: We know that the V(X) =E(X2) -(E(X))2 By using the  above definition of V(X), we can easily prove…

Q: 11. Answer by TRUE of FALSE each of the statements: (i) 4x³ + x² ln x¹ = O(x³). (ii) x³ + 4x + 15 =…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Determine s' (x) ifs (x) = x-7 + e-8a O s'(x)=x6 - e-8x O s'(x) = -7x-8 - e-8x-1 O s'(x) = -7x-8 -…

A:

Q: "8 does not divide x^2– 1 if x is even". prove it directly

A: We need to prove  8 does not divide x2 - 1 , if x is even. OR if x is even, the 8 does not divide x2…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.