Which of the following is NOT correct Boolean algebra rule? O O xa = a O 1xa = a a + 1 = 1 O 0 +a = a

Q: Let E = Q(V2,v3,V5). (1) Find 3 distinct non-trivial elements in Aut(E/Q). (2) Denote such three by…

A: Consider the given

Q: if Eo an is divergente then (a,)² is also divergente. Select one: True O False

A:

Q: Which of the following is correct? * O U(14) is isomorphic to S3 O U(14) is isomorphic to U(12)…

A: (a) U(14) is isomorphic to S3. Consider U(14). The elements in U(14) are the elements that are…

Q: o is a) 1-1 b) onto c) Both 1-1 and onto d) None

A:

Q: Given x' = acose + bsin0 y' = -asind + bcos0 using Cramer's rule, find a in term of x'and y'

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Q: 2. Let A M, (R) be given. (a) If AA¹ On, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose…

A: The objective is to prove the two given parts. Symmetric matrix: A square matrix is said to be…

Q: Q3. Give an example of two denes not equal X subsets of (R,T) and (z. of). ( Explain your answer ).…

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Q: 1. Give an explicit formula for each sn a) a, = 5an-1 – 6an-2 + 6(3")

A: The objective is to give an explicit formula for each sn an=5an-1-6an-2+63n

Q: B. Express the following quantified statements in simple English: 1. (3x) [Clock(x) A (Slow(x) A…

A: We have to write quantified statements to nr

Q: Find simpler expressions for the quantitie in Exercise

A: a. We have an expression,  2lne=2lne12=2×12lne    Using formula, lnmn=nlnm            =lne=1

Q: b. Let A and B be elements in Sn T. Show that An BE S N T. c. Let A¡ be elements of SnT for i € I.…

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Q: (a) The following are equivalent in a Boolean algebra: (1)a + b = b.(2)a * b = a.(3)a' + b = 1,(4)a…

A: (1) The given equation is: a+b=b

Q: 2. Prove the following a) If a 0 and b2 0. Then a <b if and only if a? < b².

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Q: Verify the &-ô identity: Ejkɛipq = djpôkq – djqðkp. Then use this identity to show that (a) EilmƐjlm…

A: The given identity is εijk εipq=δjp δkq-δjq δkp  where the εijk is called the alternating tensor or…

Q: 7. Let H = {1,5} and two operations * and *' on H defined as follow: 15 15 1 11 1 15 5 15 5 5 5 Is…

A: To check whether the given set along with the given operations are Boolean algebra or not we will…

Q: Prove the following:  1. if ax=a for some number a≠0, then x=1

A: Prove that, if ax = a for some number a ≠ 0, then x = 1.It is given that, a is a nonzero real…

Q: Use properties of Boolean algebra to simplify the following Boolean expression: [x' + (yz)'][x +…

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Q: 3. Prove or Disprove: Let a, b e Z. If alb² and a < b, then alb.

A: The given statement is disproved .

Q: Find simpler expressions for the quantitie in Exercise

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Q: Which of the following is not correct? O U(8) is isomorphic to U(12) O U(14) is isomorphic to S3 O…

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Q: Find the dual of the Boolean expression I +1.0+ Fyz O z. (z+1). (7+ y+z) O T. (7 +0). (7 + y+z) O z.…

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Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

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Q: ns of this assertion.

A: Exact differentials : Recall that change in internal energy , dv ,is called an exact differential…

Q: The following are equivalent in a Boolean algebra: (1)a + b = b.(2)a * b = a.(3)a' + b = 1,(4)a × b'…

A: (3) The given equation is: a'+b=1

Q: Which of the following elements of U(14) doesn't generate U(14)? 11 3 All of the above

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Q: Which of the following is correct? U(14) is isomorphic to U(12) U(14) is isomorphic to S3 None of…

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Q: Find simpler expressions for the quantitie in Exercise

A: We have to simplify the following quantity -  ln y = 4t + 5

Q: 2.5.21. Prove the following set identities. (a) (AnB)° = A°U B© (b) A\(BUC) = (A\ B) N (A\ C)

A: let x∈(A∩B)c ⇒x ∉ A∩B⇒x ∉ A or x∉ B⇒x ∈Ac  or x∈Bc⇒x∈Ac∪Bc⇒(A∩B)c⊆Ac∪Bc    ...(1)let x∈Ac∪Bc⇒x ∈Ac…

Q: 7. Let H = {3,2} and two operations * and *' on H defined as follow: 3 ** 3 2 3 3 3 2 2 2 Is (H, *,…

A: This question is about application of Boolean algebra

Q: The following are equivalent in a Boolean algebra: (1)a + b = b.(2)a * b = a.(3)a' + b = 1.(4)a * b'…

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Q: 1. Prove the next identity: A\(B U C) = (A\B) n (A\C).

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Q: Let a, b e C. (i) Prove that if |a| <1 and |6| < 1, then a - b < 1. 1- āb

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Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

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Q: Find the Boolean product AOB where A and B are defined below. [1 0 1 A = 0 1 1 1 1 0l [1 0 1 B = 0 1…

A: Here given that                           A=101011110       and       B=101010100 We have to find…

Q: Which of the following is correct? U(14) is isomorphic to U(12) O None of these O U(14) is…

A: Fourth option is correct.

Q: 8. Write a formula of P that is equivalent to the following formula, but which involves a different…

A: To find- Write a formula of P that is equivalent to the following formula, but which involves a…

Q: Which of the following is correct? * O U(14) is isomorphic to U(7) O U(14) is isomorphic to U(12)…

A: (NOTE- There are two different questions given. According to our to policy, only required to do the…

Q: 69. If a>0, h>0 and ne N, prove that there exists 0, 0<0< 1, such that h? (- 1)" - ' h"- ! 1 1 h (-…

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Q: [1 Which of the following values of a will make 2 Lo 2 2 a non-invertible? (А) 1

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Q: Evaluate the Boolean power AB where 1 1 A = |0 1 0 1 0

A: Given matrix is: A=101010110

Q: The following are equivalent in a Boolean algebra: (1)a+b=b, (2)a*b=a, (3)a'+b=1, (4)a*b'=0 i.…

A: The given equations are,1a+b=band2 ab=aWe need to show that these twp are equivalent.

Q: 2 Which of the following values of a will make |2 0 a non-invertible? -al

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Q: Which of the following is correct? * O U(10) is isomorphic to U(12) O U(10) is isomorphic to U(5) O…

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Q: 11 1 1 0 1. Given: A = 1 1 1 аnd B 3D |1 1 1 Lo ol a. Find C, the boolean product of A and B. Show…

A: given A=001110111100 and B=011100 a) find C, the boolean product of A and B. b) find the meet of C…

Q: and lo le elemento fa boolean Algehna 6 Yt a Lot a06 = ab + a'b' (kquivelence"). Prove that laob)oc…

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Q: prove the following if 01

A: Suppose a∈ℝ such that 0&lt;a&lt;1 If possible, let us consider that a2&gt;1 Now,…

Q: Which of the following is correct? * O U(14) is isomorphic to U(12) U(14) is isomorphic to S3 O…

A:

Q: 28. Find the Boolean product of A and B, where [1 0 0 17 A =0 1 01 1 1 and B =

A: A=100101011111B=10011110To find A⊙B

Q: 4.89. Let a E Z. Prove that if 3 5a, then 3 a.

A: Given, 3 divides 5a.  Then, we can write 5a = n*3, where n is an integer.

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!