6. Prove: If alb and a|e then a|(b? -4c) 7. Prove: if ab then a? \b

Q: 3. Prove that (An B)² C A × B.

A:

Q: (2) (a) Show using set identities that AUBU(AN BNT) = AUBUT (b) Prove by contradiction that if A C…

A:

Q: 7. Show that if A and B are similar, then det A = det B. %3D

A:

Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: If a, bEZ such that a b then the numbers a and b are called relatively prime numbers if ged (a, b)…

A: True

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

A:

Q: 2. Prove: A – B = ANB

A:

Q: discrete

A: Let a and b be the integers.It is given that if a|b or a divides b then a2 must divides b2 that  is…

Q: 8. What statement could be used to prove that m n? O 24살 26 O mz1+m 22= 180° O mZ3 + m = 180° O 22쓸…

A:

Q: 12+1 To prove that if <1, then r 12+2 <2. If r€Q+ r

A: It can be solve using method of contradiction

Q: Suppose that a and b are two numbers with this property: for anv e va it is true that azb. Prove a =…

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Q: I elements is A, then the

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Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof,…

A:

Q: Disprove by Contradiction If a,b,c ∈ ℕ, then at least one of a-b, a+c and b-c is even.

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Q: Discrete math

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Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

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Q: 4. Let A C BCR. Prove A° C B°.

A:

Q: 75. If f(7) = 13 and fis one-to-one, what is f(13)?

A: For a function domain is set of values for which the function is defined. The range of a function is…

Q: a. Used by competitors o. That does not currently exist in a organized form :. That already exists…

A: Secondary data is known as the data that are collected through public sources, i.e., census,…

Q: 1. Prove: Va, b, c E Z: alb and blc = alc 2. Give an example with a = 7 and b, c + 7.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2. Prove the following statement directly. V a, b, c e Z, if a | b and a c, then a | (7b + 4c)

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Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

A:

Q: If a1, az, az,.-ans. be the A.P. and S, = a-1m+1+a-1m+2+a-1n+3 +.--+ am %3D Prove that :…

A: In this question we have to proof S1, S2, S3,.... are in Arithmetic Progression.

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: Prove that ord,(a + b) > min(ord,a, ord,b) with equality holds if ord,a ± ord,b.

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Q: (7) For any nonzero a, b € Z, the gcd(a, b) divides the lem(a, b). (8) If r, y € Z and 3 divides ry,…

A:

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

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Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

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Q: 5. If A = I then what is A?

A: Here given as A2=I Taking determinant both side A2=IA2=1A=±1 Thus A is non singular and inverse of A…

Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: Disprove: For all integers a,band c, if a|(bc) then a|b and a|c

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Q: how that Q(√2 + √3) =Q(√2,√3).

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Q: 2 Determine if the following statement is true or false. Motivate your answer. If Re(:) > Re(w) and…

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Q: [1 2] If A = then show that |24|=4||| %3D 4 2

A: Introduction :We have given a 2*2 matrix A. We have asked to show that |2A| = 4|A|.

Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

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Q: Prove (without expansion) b a c d a -d = (a? + b? + c? + d?)? d -b -c a |-d -c b a

A: We have to prove that abcd−ba−dc−cda−b−d−cba=a2+b2+c2+d22 Consider the left hand side expression…

Q: a If 2" = ア,what is

A: Taking log both sides of the given equation

Q: 9) Determine whether AMNO = AQRS. Explain. M(0,-1), N(-1,-4), 0(-4,-3), Q(3,-3), R(4,-4), S(3,3)

A: Given, M0,-1;    N-1, 4;    O-4, 3Q3, -3;    R4, -4;   S3, 3 We have to determine whether  ∆MNO…

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

A: Recurrence relation - it  is an equation that denotes  the nth term of a sequence as a function of…

Q: Prove: Let a, b, c, d be real numbers. If a &lt; b and c &lt; d, then a + c &lt; b + d.

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Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

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Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

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Q: 2.3.12 Which of the following statements are true? Explain. (a) 3 a married person x such that V…

A: 2.3.12 a) is False Since, the statements says that there exist a married person x such that for…

Q: 2. Use prove by contrapositive to show that: (For real numbers a, b, c) If (a – b)² + (b – c)² + (c-…

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Q: (a) For integers a, b, q, r, prove that if a = bq + r then (a, b) = (b, r).

A: Since you have posted a multiple question according to guildlines I will solve first(a)    question…

Q: 2 E AUB implies that 2 E A and 2 e B. Select one: O True False

A:

Q: prove that if a>4 then (a-2)^2>4

A:

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!