(f) A = R, P = {S,: y e R and y > 0}, where S, = {x e R: x < y} %3D

Q: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers…

A:

Q: 4. (а) Let a, b, c E Z. Prove that, if a | b, then ac | bc, but that the converse may be false. (b)…

A:

Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

A:

Q: 2. Assign Hermit's interpokting tolynomial by The fallowingy da ta:

A: The Hermite's interpolation polynomial is H(x)=∑ui(x)⋅yi+∑vi(x)⋅yi'. Here…

Q: Is L = {x+ix : x ∈ R} an open subset of C? A closed subset of C? Both? Neither? Justify your answer.…

A: To analyze : The subset L=x+ix : x∈ℝ ⊂ ℂ

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: Lot A and B be ovents such that P (A) = 4/5, P (B) = 1/3, P (AIB) = 1/6, where A' is the complement…

A:

Q: 4. Find the degrees of the following extensions. (a) Q(√3) over Q. (b) Q(√3, i) over Q(i). (c)…

A:

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

A:

Q: Prove the following: P(n,r)=P(n-1,r)+r.,P(n-1,r-1)

A: Recall: P(n,r ) = Prn=n!(n-r)! n! = n(n-1)!

Q: all your calculations and simplify your answer completely. Il you only give a final an- Swer you…

A:

Q: What is the domain of h? ) (-2-1, 1, 5 and 6) 25x56 D (5-26, and 7)

A:

Q: Suppose n lines are drawn in the plane in general position, meaning that no three lines intersect in…

A: The problem is essentially a planar graph coloring problem.In graph theory, a planar graph is a…

Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

A:

Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: 8. Which of the following is a derived rule? • A→ BH (3x) A → (3x) B • (Vx) (A → B) + (3x)A → (3x) B…

A: Please visit the next step for details

Q: Determine whether the following sets are convex (1) {(x,y)=√x + √√]]l}

A:

Q: What meaning can be attached to this cross product: r the toolbar, press ALT+F10 (PC) or ALT+FN+F10…

A: The cross product of two vectors A→ and B→ is given by; |A→×B→|=|A→|×|B→|×sin θ And the cross…

Q: ~ on R? by (x, y) ~ (u, v) if and only if ? + y? = u² + v2. In class, we saw that this defines a…

A:

Q: 6. Show that there is a one-to-one correspondence between the Cartesian products A x B x C and A x…

A:

Q: 4. Find a translation that maps A(2, –3) onto B(4,–2).

A: Given that: A(2, -3) and B(4, -2)

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: ere any way the work can be shown out?

A: The first line producing 0.10 The second line producing 0.27 The third line producing 0.63…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.