|u| = |v| show that (u + v) • (v - u) = 0 is logically equivalent to condition u⚫u=v•v

Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: (a) please find the value of A and B  (b) The support of (U,V), namely the values of u and v that…

A: Given,and..To find the value of A, and the support of..

Q: Premises: Vx(L(x) → H(x)) 3x (~ J(x) A L(x)) Conclusion: 3x (H(x) A - J(x))

A: Given that Premises:      ∀xLx→Hx                        ∃x~Jx A LxConclusion:  ∃xHx A ~Jx We have…

Q: 4. Let aj = 9. and b = 63 , a2 = 45 (a) Write b as a linear combination of a1 and a2. b = aj + a2.…

A:

Q: EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

A:

Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

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: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: O show that 2. I| a+ V 1= 11 + 1i if and only if ū. ů =0 %3D

A:

Q: Prove that xJ(x) = vJ , (x)– x (x) X V. v+1

A:

Q: Let u = and v=. (a) Find ||u||. (b) Find u – 3v. -

A: Given: u=1,4,3  and v=2,0,-1

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

A:

Q: Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k = 0

A: To Determine :-  The real numbers x , y and z  such that   x + 4  i +  y -5  j +  z - 1  k =0

Q: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

A:

Q: Give an example of a nonzero vector x ∈ R2 forwhich||x||∞ = ||x||2 = ||x||1

A: Let's first define what each of these norms means:   The Euclidean norm or L2 norm, denoted ||x||2,…

Q: a(k) = eak coshw.k coshw, k ewok te-wok 2 eak coshw.k eak ewokteake-wok 2 X(Z) 3D글 z(enk e.k) + 글…

A:

Q: 1. Translate these statements into English, where the do- main for each variable consists of all…

A: a) for all x, there exists y such that x is less than y b) for all x, for all y if (x is greater…

Q: If |ū| = 4, |v|=5, |ū-v=6, determine |ū+ v.

A:

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

A:

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

A:

Q: Let u (41, U2, Uz). Explain why u•u > 0. When is u•u 0?

A:

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

A:

Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: Show that u and v are orthogonal if and only if ||u+v|| 2 = ||u|| 2 + ||v|| 2

A:

Q: = [4, 3, 0] v = [-2,0, –3] u = u x v = Ex: 5 Ex: 5 Ex: 5

A:

Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

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: Prove the following: a) Show that ||ū + ở|| < ||ū|| + ||7||. b) Show that ||ū x 3||² = (ū ·ū)(³ · 7)…

A:

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3<…

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: Either prove that the wff is a valid argument or give an interpretation in which it is false. [(Vx)…

A: Given that, For all x P(x) implies that for all x Q(x).

Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

A:

Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Which of the following statements is correct? a) P(X | Y) = P (X) if X and Y are independent.

A: Our aim is to find the correct statement.

Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

A:

Q: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

A: We have to write in u(x,y) and v(x,y) form.