Let a, b, c EZ s.t. ab and at c. Prove that af (b+c), and clearly state which method of proof you choose.

Q: Show that if ac|bc, then a|b.Show that if a|b and b|a then a=±b.

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Q: .Prove that A =B² = C² =I. 0 -1 Given A = B = and C = 1 0 i

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Q: For which of the following is it true that n(A) + n(B) = n(AUB)? a. A = {a,b,c}, B = {a,b} b. A =…

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Q: given A={x I x2 - 1 = 0 }, B = {x I x2 + x - 2 = 0}, and C = {x I x3-x2=0} A, B, C Ⅽ R a. A U ( B ∩…

A: A=x:x2-1=0B=x:x2+x-2=0C=x:x3-x2=0 Then we have to evaluate A∪B∩C.

Q: 2) find I oP frthe following Aable 14 XI 5 3 fi 16

A: To find: The Interquartile range. IQR = Q3 - Q1

Q: If u x v=u x w and if u #0, then v =w. Select one: O True O False

A: Given u*v=u*w Is v=w True or false?

Q: Date: Name: Given: BA BC and DA = EC Prove: BD = BE Statements O PA BC 2 BA= BC and DA= EC 3 BD + DA…

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Q: If u = 7 then uu? and u'u =

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Q: Four different triangle congruence postulates are SSS, AAA, SSAA and AASS. O True O False

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Q: 1 2 0 1 1 2 4 If A = B = 1 and C = 0 2 1 then (CB")" + A"= Select one: 12 5 OA. 7. 12 5 OB. 3 C.…

A: We have to choose  the correct  option by doing the correct option.

Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: Can I please get further clarification? It is difficult to follow the work and we know for sure a is…

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Q: a) If a2 is even, then a is even. (b) If a|b and a|c, then a|(b − c). (c) If a|b and c|d, then…

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Q: 9f a,b,c,d EN & a = b frod n) C=d(modn) sherw that bd(radn)

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Q: 3 4] 2 and ||A||, = 17 , then k= -2 k. If A = ||k|+1 1 -1 Select one: а. 11 b. 14, -14 С. 11, -11 d.…

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: are in A.P., b, c, d are in G.P. and at a, c, e are in G.P. -10 - e

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Q: 8. If å = [1,3, –1] , b = [2,1,5] and i = [-3, y, z] Find the value of y and z if å x i = B a) Find…

A: We have to find the cross product of the vector.s.

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: Q.1) Evaluate IT ycos(ry) dzdy 0.

A: We will find the double integral as following.

Q: 6. For A, B, subscts of R, define A+B= {a+b:a€ A, bE B} and A B= (ab:a € A,bE B} (a) For A=…

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Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: True or false: a. If we reject Ho, then we conclude that H, is false. b. If we do not reject Ho,…

A: If the Null hypothesis is rejected it means alternative hypothesis is accepted and null hypothesis…

Q: Given that P = () and Q: = () Then: P + Q =

A: solution is given below.

Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

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Q: Y D Prox

A: Product of two sets

Q: 5. If and A = 5 3 -2 2 7 -1 521 verify that A(B+C) = AB+ AC. 6 5 1 C = 107 B = 2 0 " TOT

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Q: Prove that A N (BU C) = (A N B) U (A N C) by giving a Venn diagram proof. Label your diagram(s)…

A: Venn diagram are pictorial representations of mathematical or logical sets of data as closed curves…