6. Let a1, a2,...,an be distinct positive in not containing s = a₁ + a₂ + + an. A grassh A AL icht mitl with 1.

Q: U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die that are…

A: Given If U is the set of the numbers on a 6-sided die and B is the set of numbers on a 6-sided die…

Q: -25 (1+j2 2-j5 ) = 57 + j24 2 \3+j4

A: We need to simplify the expression -2521+j23+j4-2-j5-j and show that it is equal to 57+j24 Consider,…

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: 12.2 Determine Lu+2v),luvi and afuxv} for Ve) = (4t,,5-t)

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Q: 10) If 1+ abt = c where a, b, and c are positive, determine the value of t. %3D

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Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

A:

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: 42. If P (A) = 0.5, P (B) = 0.40 and P (A UB) = 0.70, find P (A/B) and P(A U B) where A is the…

A:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Given that x>0 and y>0 proof that xy>0. (x,y are integers)

A: Given that x>0 and y>0, then to prove that xy>0. x, y are integers.

Q: A. j2n = (-1)" B. jan+1 = j C. j¯" = (-j)" D. jan-1 = –1

A:

Q: if U ={1 2 3 4 5 6 7 8 9 10} A={1 3 5 7 9} B={1 2 5} what is A'? what is B'? what is A'uB'?

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Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

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

A: Dot product gives a scalar value  .

Q: if zi = ayi for i=1,2,...,n, show that z=ay

A: Here we have given that if    then we have to show that   so here zi and yi are random variable…

Q: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

A: Given, x3≡amod p At p=7 We know that suppose p is rational prime p≡1mod 3 then x3≡a mod p is…

Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: X2/ Suppose sr=20142} and c-{ {o8} Enumcrate the cLass of all 6-tields Containing and give cce)

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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Q: 9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

Q: 2 1] Assume A = 1 3 4. [2 2 4 and B = show that (AB)' = B' A' [3 6 4]

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Q: 33. What is the real part of In (2 + j2)? a. 0.785 b. -0.785 c. 1.040 d. -1.040

A: 2+j2=2√2(1/√2 + j/√2) = 2√2(cos(π/4)+jsin(π/4))

Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

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Q: Find proj,u and scal,u by inspection without using formulas.

A: Given the graph

Q: 4. Let 1-a a P = 0 < a, b < 1. 1-6 Prove (:) (1 – a – b)" 1 b a a -a a +bb a a +b -b b

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Q: 26. Let A=61] Find a) A V B. and b) Α Λ Β. B = [id] c) A OB.

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Q: Suppose x, y, z E R. Show that zz = yz if and only if either x=y or z = 0.

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Q: Q3) Assume A = [4 16 3 11 7 21 [3 21 and B = 1 5 (3 14 3 show that (AB)' = B' A'

A: Given, A=431672B=321543

Q: Prove that for а + —1,а > 0, пENis (1+ а)" > 1+ па.

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Q: 7. Let U = {-5,-4, -3,-2,-1,0, 1, 2, 3}, A = {-1,0, 1} and B = {-4, -2,0, 2}. %3D Prove that (A U…

A: Explanation of the answer is as follows