Let A = {p ∈ Z|p = 2r - 6} where r ∈ Z, and let B = {s ∈ Z|s = 4t - 4} where t ∈ Z. Show |A| = |B|.

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

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Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: 11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If…

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: et z = 6ex²y³ find O 12xy³ex²y³ O 18x²y²ex²y³ O 18xy³x²y³ O 12x²y²ex²²³ дz ax

A: Given, z=6ex2y3

Q: Show that For all z E C, with z # 0, then: |z/²z=1 = z

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Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: 1 - Be X and Y variables independent with o ²X variations and o2²Y, respectively. Being Z=X+ Yand…

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Q: Let u, ER" prove that ||ū + ï|| ≤ ||ū|| + ||v||

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Q: Let v = (−1, 2, −3, 0, 5)T . Find numerical values of ||v||1, ||v||2, ||v||3, ||v||4, and ||v||5.

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Q: Show that for all v in Rn, II v II s <= II vII m·

A: vs represents the "sum norm" or "L1-norm" and vm represents the "max norm" or "L infinity-norm".To…

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: Show that S= {xER*| x < 2x.} IS convex

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Q: Let A ∈ Rm×n and B ∈ Rn×r . Show that ||Ax||2 ≤ ||A||(1,2)||x||1 for all x in Rn.

A: To prove that ||Ax||2 ≤ ||A||(1,2)||x||1 for all x in Rn, we can use the Cauchy-Schwarz inequality.…

Q: LET Z Z₂ = FIND ZI 리 Z₂ 8+31 9-21 AND Z₂ Z₂

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Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

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Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

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Q: Let r ERQ. Prove that for all a, b, c EQ, =cr iff a = 0 and b = c. a + br

A: Given that r∈RQ Let a,b,c∈Qa+br=cr iff a=0 and b=c

Q: Check that P ˅(Q ˅ R) is equal to ┐(R ˄ Q ˄ P) → P

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Q: Let z дz ?x дz ду = = Gexy³. Then:

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Q: If P(A/B) = 0, then A &B are: Select one: a. Mutually exclusive b. ACB с. ВС А d. Independent

A: There are two events A and B such that PA|B=0 PA|B=PA∩BPB=0 Therefore it follows that PA∩B=0

Q: Find the degree of Q(V2, V5) over Q.

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Q: u = [2, 6, –5] and v= [-3,–1,6] %3D A · A + (A + ng-) · (A x n)

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Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: Is 1z = 1 for all z ∈ C?

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Q: Let A = {m ∈ Z|m = 4k + 8} where k ∈ Z, and let B = {n ∈ Z|n = 2r + 2} where r ∈ Z. Show |A| = |B|.

A: Let A = {m ∈ Z|m = 4k + 8} where k ∈ Z and let B = {n ∈ Z|n = 2r + 2} where r ∈ Z.  We now show that…

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

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Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

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Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Evaluate JIS ₂x+ydV where B is the box determined by ze B 0≤x≤ 1,0 ≤ y ≤ 3, and 0 ≤ z ≤ 5. The value…

A: Here we have to evaluate the volume integral over the given volume region.

Q: ). Find 1 |z-j|=2 Z

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Q: Ho We By the Same wayprove e that : X J, (x) V+1 xp

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Q: Let x ∈ R. Prove that if x 0.

A: Given :

Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: Let S be the set of integer solutions to the equation ri + r2 +13+x4 = 30, where ri >0 for i = 1,2,…

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Q: Let A = {y ∈ Z : 2<y ≤ 14 and y is even}. What is |A|?

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