1 Premises: p → (q ^r), s → r, r → p. Prove: s → q. 2 Premises: -(r v s), ~p → s, p → q. Prove: q.

Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: Compote clerivative bao fx)= cot(x), x=0.8 flx)=cot(x, %3D fl0.8) =

A: We use basic inverse trigonometric identity.

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Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: of is: If f(z, y, z) = ry z' + In (z) In (y²) In (z³) then dz

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Q: Prove by induetion onn that for all irdegers nz2, Nz2,Gilit)

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Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

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Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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Q: let X=R and R={Caro): a ER 3U {8IR3 C Right way totolyy) c heck Ris

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Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Suppose ū = (–5, −4, −5) and v = (–2, 4, −5). Then u x vis Uxuis and

A: Topic- Cross Product of Vectors

Q: If (X.r) and (X,r,) are T,-spaces, then (X.r,nt) is also a T, -space. GOOD LUCK

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

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A: Here we have to find the ratio between two sides such that the given 2 triangles will become…

Q: 6. If u=,%) prove that xu, + yu, + zu, = 0

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: Show that if Y = ax + b (a = 0), then Corr(X, Y) = +1 or -1. We know Cov(X, Y) = Cov x, ])--)-I + b…

A: We need to show that, If Y=aX+b then Corr(X,Y)= +1 or -1

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: If divF (x, y, z) = 0 for all (x, y, z), then curlF (x, y, z) = (0,0,0) for all (x, y, z).

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Q: 1. What congruence postulate/theorem cannot be used to prove that ALIV AJIN given that LVis parallel…

A: topic- congruent triangles

Q: If (X.r,) and (X,r,) are T.-spaces, then (X.r,nr,) is also a T,-space. GOOD LUCK

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Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: b)use Cauchy Schwarz inequality to show that if Let u = and v = inequality to show that a² + b?

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Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.

A: we have to partial derivative with respect to u by using chain rule

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: Prove that if PQ≅RS and RS≅UV then PQ≅UV in the simplest way possible. Please do not use any example…

A: Congruent relation is an equivalence relation. So, congruent relation is a reflexive, symmetric and…

Q: Do not use the inference rules Transposition, Resolution, Contradiction, Idempotence or Identity. Do…

A: given premises 1) x~Ax⊐Dx 2) Ey~By∨~Dy⊐ ~~Dy∨~Ay 3) xAx∨Dx⊐~Ax∨~Dx /ExAx∨ Bx

Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: prove that dv v 21/12 الله duz 2 2

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Q: 3. Prove that: na” u[n] = az (a-z)2

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Q: Prove that zU LX Statement Reason 1. y XV 1. Given 2. yz VW 2. Given 3. uz e WX 3. Given 4. VZ = YZ…

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Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

Q: 9. For n = 1,..,n, let X, be independent r.v.'s such that %3D P(X,=1)= p,, P(X,=0)=1- p,- Under what…

A: Hello! As you have posted the different questions, we are answering the first question (9). In case…

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: prove with a table if x → y then xor y xor y = y

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Provide example

A: Consider that x is orthogonal to v and w To check is it true that x is also orthogonal to v − w.   a…

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra

Q: Prove that (u + v) · (u - v) = llull2 -llvll2 for all vec­tors u and v in Rn.

A: Consider the given Vector equation, u+v·u-v=u2-v2 Here the objective is to prove that the…

Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

A: