if a:b=c :d prove that (abcd)(a²+b²+c²+d²)=(a²+b²+c²+d?)

Q: Given A,B and C required to prove that A\(B\C)=(A\B)U(A∩B∩C)

A: Given  A, B, C are any three sets  We have to prove  A\(B\C)=(A\B)U(A∩B∩C)    Let X be unversal set…

Q: If i = 5+2, à = x - ỷ and b = j – z , show that a =

A:

Q: Show that if AB = AC and A is nonsingular, thenB = C.

A: Given that  A is invertible matrix. It means inverse of A matrix is possible. A is non-singular…

Q: Prove that if A2 = A, then I − 2A = (I − 2A)−1.

A: Let A2=A To prove :  I − 2A = (I − 2A)−1

Q: Prove that AABC A DEF. C=12. D2,4) E(4, 2) 6-14.214 A6 4)

A: Compare the lengths of both the triangles.

Q: Let A = {x ∈ Z | 6 divides x} and B = {x ∈ Z | 3 divides x}. Prove that A ⊆ B, and then prove that…

A: We can prove using like showing every element in one set is an element of another set like that.

Q: 4. Given that AB || CF, m²E = 48 ° and m¿B=78º, %3D Prove: m²F=30° A 78° 199

A: Given query is to proo measure of angle F is 30°.

Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: Assume that u v = 6, ||u|| = 3, and ||v|| = 2. What is the value of 6u· (4u – 4v)? -

A:

Q: Prove that the operation * defined on M2x2(R) by taking A * B = A. B V A,B E M2x2(R). %3D is an…

A: Given that A*B=A.B ∀ A, B∈M2×2(R)

Q: Prove that if A – B – D and B – C – D, then A -C– D.

A:

Q: prove that: DO e de a e +6 2/3 cwhere a, b > o

A: Where a, b>0

Q: Prove that for all a, b, and c e Z, if a † (2bc+12), then a † (b – 2) or a ł (c + 3).

A:

Q: Given: Prove: A AB || DC AF = EC BE || FD B KABE CDF E F D C

A: Question is solved.

Q: BC = a. Prove: AB = 2a and AC = aV3. %3D %3D

A:

Q: Write a two-column proof to show that if WXY ABC, then WXY = ABC. L W A X Given: WXY ABC Prove: ABC…

A: Given ∠WXY≅∠ABC The statements are listed in a column on the left, and the reasons for which the…

Q: all that apply. Wing are Selec B. O A. mDB 0D. ZBDE LBED mDE mAC mAB E. ZBDE ZBAC B. mDB mBE mAB mBC…

A: Solution:-

Q: Show that SU2(C) is simply connected and SO3(R) = RP³.

A: Consider SU2C group  SU2=α-β¯βα: α,β∈ℂ,α2+β2=1 To show it is simply connected we will show its…

Q: If z, = 1+ jb , Z2 = re¯)² , z1/z2 = -10, determine all possible values of b and r.

A: Consider the provided question,

Q: Given: AB s BC, AF = KC, MZDKA=mZEFC Prove: AD = EC В D А F K C er: mZA = m2 by reason AADK = A by…

A: topic - congruence of triangles

Q: Which statement proves that ry? a b. 1/2 3/4 5/6 7/8 y 9/10 11/12 13/14 15/16 O 22 is supplementary…

A:

Q: In the diagram below ABGH, BCFG and CDEF are squares. Prove that 21 + 2 = Z3. A В C D <4 <6 <5. <7…

A: GF/DF =1/√2 FD/FH=√2/2 = 1/√2 So, ∆GFD~ ∆ DFH Angle 1= angle 6

Q: Let A, Be M, (C) be positive definite. Prove that (4+ B)" s(A" +B").

A: Let A,B∈Mnℂ be positibve definite.  To prove A+B-1≤14A-1+B-1 Since, A and B are positive definite,…

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: In AABC, AB//QR and AP : PB = BR : RC. With reasons, prove that PQ//BC. R C

A:

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

A:

Q: Complete the proof that AUVW = ATXW. W V Statement ZUWV LTWX VW I UV 3. WX 1 TX 4 VW WX 6. AUVW E…

A: ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles…

Q: If (x+iy) = a+ ib, Prove that + a b = 4(a -b*).

A:

Q: 2. Suppos hour ar a. Wn BLOS b. Writ i. ii. 3. A contra common a. Wri b. Write i. i.

A: Any linear programming problem in two variables can be solved by identifying two inequalities that…

Q: Prove (A = B) = (A v C) = (B V C)

A:

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: 1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C)…

A:

Q: Let a, b,c € R4. Prove that c+a a+b b+c c+b a +c b+a Al

A: a,b,c∈ℝ+ab+bc+ca≥c+ac+b+a+ba+c+b+cb+a

Q: C) prave that sbatz = Clnrtt - an for all nE B, Nzl. %3D |

A: We will prove the relation of part c by mathematical inducation.

Q: Use the following problem: Given that Z1= Z4, prove that 22 = 23. 3 Write your proof (in any…

A:

Q: 1. Which side is needed to prove that ARAG E ACML? G C R M.

A:

Q: prove that a(a+b)=c(c+d). a b d

A:

Q: Let z, w e C. Show that |2 + w? + |z – w? = 2(|2|2 + |w?). %3D

A: We will show the given result.

Q: (а-b) a (b-c)* 3 d

A: a, b, c, d are in continued proportion Therefore, we have ab = bc = cd = k (say) c=dk, b=ck=dk2,…

Q: B) Prove that (A + B) +(C + D) = (A+B) (C+D) %3D

A:

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: Let z, w E C. Show that |z + w[? + |z – w|? = 2(\z|² + |w|?).

A: Any complex number, Z can be represented as Z=x+iy, where x=Re(Z) , y=Im(Z) . The expression, Z can…

Q: Q1: Prove that ; If CE AB, D E AB and C# D, then CD = 2 %3D

A: Key point: 1. There is only one line possible from two distinct points.2. The line is expressed in…

Q: 3.1 Prove: For all a and B in R, Ja + B] > | |a| – |B||. Hint: la + B] = |a – (-B)|-

A: Answer is in below steps.

Q: Prove that if C is equivalent to B and B is equivalent to A, then C is equivalent to A.

A: The relation 'R' = 'is equivalent to' is transitive. Therefore if x R y and y R z then x R z.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.