Using the Mean Value Theorem, we can prove that a. 2* > 1+ xln2 for all x > 0 b. 2* <1+ xln2 for all x > 0 c. 2* = 1+ xln2 for all x > 0 d. 2* > 1+5xln2 for all x > 0 e. None of these а. O b. с. d. O e.

Q: What are the possible number of Boolean functions with n-ternary variable?

A: We have to state the possible number of boolean functions with n-ternary variables.

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: Suppose that n pigeons are placed into m holes with m ≥ k(n+ 1) for some positive integer k. Suppose…

A: See the attachment

Q: 4. /xln2xdx хрх

A:

Q: Find all natural numbers in such that n²<z". Prove your assertion.

A:

Q: If X~N(2,9), compute a. P(X>=2) b. P(1<=X<7) c. P(-2.5<=X<=-1)

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: Show that 1+2+3+… +n = (";").

A:

Q: Determine the least upper bou You must fully justify your an

A: We have to find least upper bound of the given set

Q: (2) Is the set {r € Rr² € N} countable? Justify your answer.

A: Yes the set A={x €R : x2 €N } is countable

Q: Q.3 Explain operations on classical / crisp sets

A: There are various operations on Classical sets.   The first kind of operation is Union. The union of…

Q: If a set S has n > 3 elements, how many subsets of S have more than one element, but less than n…

A:

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

A:

Q: If N={1,2,3), then (xlxEN< ? }

A: Given :- N = {1,2,3} Then {x | x ∈ N &lt; ?} Here , N &lt; 4 So, {x | x ∈ N &lt; 4}

Q: 3. From Fermat's theorem deduce that, for any integer n 20, 13| 1112+6 + 1.

A:

Q: 11. (a) What does the symbol n! mean? Find 5!. (b) Define (), and find (2).

A: To find 5! and to find the value of 52

Q: (2n- 2. Give a combinatorial argument to show that k- ways the number of ways to select a committee…

A:

Q: prove the following identities k(nk) = (n-1k-1) (n0)+(n1)+(n2)+ .... ..... +(n n-1) + (nn) = 2^n…

A:

Q: Let & € N. Prove by using the contra-positive that if ³ is odd then x is odd. Proof: Choose the…

A: Introduction: Contra-positive method is the way to prove a mathematical statement. Every conditional…

Q: Prove that n! > 2" for n 2 4.

A:

Q: are 51 software students taking Let pi, p2,.. Psi be their final cam scores. Hence, cach p, is an…

A: Given that p1, p2, p3,..., p51 are the final exam scores of 51 software students who are taking MATH…

Q: 4. If 1 8! + 1 X find x. 9! 10!

A:

Q: **For what c value is (x-5) a factor of x³ + 2x2 + cx + 10

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: 5.2 Any lower Lebesgue-Darboux sum does not exceed any upper Lebesgue-Darboux sum i.e. for any two…

A:

Q: 2 if and only if x = -| -/-

A:

Q: Find U4,, Ñ4, , if A, = {0,1, 2, .}, A2 = {2,3, ...}, ., An = {n,n+ 1,. %3D

A: For 1st part we have A1 U A2 U......An ={0,1,2,3,.........}

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

A:

Q: . Let n be a positive integer. Prove that 1 · ( n/ 1)  + 2 · ( n/ 2)  + . . . + n ·  (n/ n) …

A:

Q: integer of the form okts is also but not' conversely

A:

Q: Suppose that µ is the measure defined in item 3. What is µ(O) where O is the set of natural odd…

A:

Q: [0,342 -0,93 -0,2581] -0,93 -0,342 0,965 5,2 0 0 x = ?y=? z=? JE]- 105,3 -284,49 -1255,8]

A: The given system is:.If the given system is: , then the augmented matrix is given by:.So, the…

Q: Problem2 Let n and k be integers with 1 ≤k≤n. Show that 2+2 ( 7 ) ( k ² ₁) = (²²+²7). 2 Σκ=1 - (²72)

A:

Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

A:

Q: 3. How many permutations of the letters ABCDEFGHI contain the strings ABC and GHI (1 Point) O P…

A:

Q: 6. For any positive integer n > 1 one has: (2n)! (n!)² n+1 <

A:

Q: 13. 10n- 9 > -59 and n - 6 < 3 |

A: Using simplification,

Q: For how many integers n with 0 ≤ n ≤ 100 is the quantity integer? n(n-1) (2n-1) 12 equal to an

A:

Q: hen Let here a11 = , 923 = , 912 = " A = A-¹ a31 = = 1 1 all a21 a31 8 8 -8 , a13 = a12 a22 a32 " 0…

A:

Q: (6!)! (3!)! = x! x = ?

A: Formula:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.