assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =  2) Pr[B|A] =

Q: 4. Prove i × (i × Ã) +j× (j × Ã) +kx (k × Ã) = –2Ã.

A: Our Aim is to prove that:-i⏞×(i⏞×A→)+j⏞×(j⏞×A→)+k⏞×(k⏞×A→)=-2A→-(i)

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

A:

Q: Let A = {x Rx ≥ 5 and x 8 and x < 12} (a) Find (AUB) nC. (b) Find An BNC. (c) Find Ce

A: Sets

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 A u (B n C) = (Au B) n (A u C).

A:

Q: Let u = Al 2 [R and v= find a and b such that au + bv [:] 3

A:

Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

A:

Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

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

A:

Q: Evaluate (t – 4/i +t-')dt

A: Given : ∫t -4t + t-1dt

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

A:

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

A:

Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

A:

Q: VXVYP(x,y) is equivalent to VyVxP(x,y). O True O False

A: ∀x ∀y Px, y is equivalent to ∀y ∀x Px, y.

Q: [x +1 0 2 1 2 (3)if A = 3 1 and B = 3 y -5 4 -1 -5 4 z - 4. Find x,у аnd z.

A: If two matrix A and B are equal then Each matrix of A and B has the same number of rows. Each matrix…

Q: Consider the set H := {a + bi + cj + dk | a; b; c; d element of  R} such that (i) i2 = j2 = k2 = -1,…

A: Here the set is given by H:=a+bi+cj+dk|a,b,c,d∈ℝsuch that(i) i2 = j2 = k2 = -1,(ii) ij = k; ji = -k;…

Q: Evaluate f (x + y − z)² dV for the box B with dimension: [0, 6] × [0, 4] × [0, 3]. (Use symbolic…

A: Solution :-

Q: 1 Assume that Pr[A]=0.45 Pr[B]=0.65, and Pr[A∩B]=0.25  A. Pr[B Compliment ∩ A]= B. Pr[A Compliment…

A: Given, Pr[A]=0.45 Pr[B]=0.65 Pr[A∩B]=0.25

Q: ASTR n = 2x+y 121 x,y € Prove that A is not open and not closed. Q

A:

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: Prove or disprove: If (xn) and (yn) are subsequences of each other, then xn = yn.

A: Definition: Suppose ann∈ℕ be a sequence. A subsequence of this sequence is a sequence of the form…

Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.