2. Prove the following statement directly. V a, b, c e Z, if a | b and a c, then a | (7b + 4c)

Q: 23. Given that 4sinh - 2coshx = Ae*+ Be* then A and B are respectively А. 1,-3 C. -1,-3 В. -1,3 D.…

A: Topic- trigonometry

Q: Is the following statement true or false? ) ) = OC) Vk, m, n e Z where k <m <n O True O False

A:

Q: 9. Suppose that Y CZ and that n(Y) = a and n(Z) = b (so a and b are numbers!). Find n(Y N Z), n(Y U…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple question, as per the…

Q: "Vn E Z+,if 30 | n² then 30 |n."

A:

Q: If a > 0 and b < 0 which of the following must be true?

A: We have to choose the correct answer from the given option according to the given condition

Q: Assume that n(U)= 85, n(A’ intersect B’)= 19, n(A’ intersect B)= 22, and n(A intersect B’)= 23. Find…

A: Given that n(U)=85, n(A'∩B')=19,  n(A'∩B)=22,  and n(A∩B')=23. We need to find, n(A∩B) and…

Q: 6. Johnny knows that AB = XY and BC =E YZ. What other information must he know to rove that AABC =…

A: If there is two triangles then they should be congruent if and only if there corresponding angles…

Q: Given that n(S) = 44, n(A) = 15, n(ANB) = 7, and n(A u B) = 24, then n(B) = %3D %3D %3D

A: Probability is defined as a number between 0 and 1 representing the likelihood of an event…

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

A:

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: If z1 and zą both satisfy z +z = 2 |z - 1| and arg (21– 2): then find Im (21 + z2). 4'

A: let z1 = x1+iy , z2 = x2+iy2

Q: 1.1 Let z, w e C. Show that |z + w? + |2 - w? = 2(|:|2 + |w?).

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: atisfies the given conditions = 30.3°, B = 38.6°

A:

Q: 6. Which set of information below would be enough to conclude that AEFG is similar to AABC? АВ AC…

A:

Q: 4. Which of the following statements is/are true. a. When o is divided by a constant, the result is…

A: In the given question we have to choose the correct option from  the given options, The problem is…

Q: Given: m<2 = 95, m<4 = 5x Prove: x = 17 3/4 5/6 7/8

A: Given: m∠2=95∘, m∠4=5x∘ According to given figure angle 2 and angle 4 are linear pair, and we know…

Q: It gER[a,b] and if h(x)=q(x) except for a finite number of points in [ab],then prove that he R[ab]…

A: The continuous set of [a,b] should be divided into finite sets first.

Q: 1. Prove: Va, b, c E Z: alb and blc = alc 2. Give an example with a = 7 and b, c + 7.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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: АР 10. In AABC, PB PQ and QC 1 If PQ = v and QB = w, express the following in terms 3 1 of v and w:…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Prove if R(a) = (21 – A)*' +hen R(1)– R(µ) = (1H)R(2)R(µ)

A: Given that Rλ=λI-A-1 Let λI-A=Aλ                      . . . (1) So, Rλ=Aλ-1 ⇒I=RλAλ=AλRλ         . .…

Q: Given the following sets, what is A U B?  U={x│0≤x≤20}         A={2x│0≤x≤5}…

A:

Q: 27. Let a, b eR 3 a> 0 and b > 0, A = (0, a) and B = (0,b). If D = {xy : x € A and y e B} %3D then…

A: Option (C) is correct.

Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

A:

Q: Suppose, X|0~ Binom(10,0) and o~U (0, 0.25), then E(Y)is equals to, a) b) 2.15 1.25 5.02 10.06

A: Answer: b) 1.25.

Q: What conclusions can yo WD DY because ZX is WX = XY because of The Find the value of x to the ne 8.…

A: Using Pythagorean therom.

Q: Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w) and…

A: We have to check whether the statements, "If Rez&gt;Rew and Imz&gt;Imw then z&gt;w" Is true or…

Q: a) By using the substitution u = √√x +3, evaluate S. 2 √(√₁ + 3)2 d. dr.

A: Given, ∫142xx+32dx

Q: Show that if 0 <y<1, and Y ~ N(0,1), we have that 9 6 3 P\Y + %(x² – 1) < =] × + (V +1). -

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

A:

Q: Nhich of the following is true? * If A = (x: x [B| |A| < |B[ |A|

A: To solve the following problem, we use the defination of cardinality of a set. Cardinality of a Set…

Q: Prove (p a q) and (T→ (¬ (p →q))) are both wff:

A:

Q: 5.12. Prove and interpret the given relations: a. ax:n E, ãx+17 A, na x | b. „Ez. |

A: Given  ax:n=Ex1 a¨x+1:n  axn|=Ax:n-Axd-Exn

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: Show that if (B) (C) = 3x N (AB)_ (BC) (CA) =y, N (A) = x, = 2x, and N N N then the value of neither…

A:

Q: (1) Show that A × B c X × Y. (2) Prove or disprove: (X \ A) × (Y\B) = (X × Y)\(A × B). (If…

A: (1) The objective is to show that, A×B⊂X×Y Given that, A,C⊂X, B,D⊂Y Now it  is known that,…

Q: If F=, and S: r=, Osus10svsa/2. Then FondA is equal to O a. 2 O b. O C. 1 O d.-1

A: Given F→=0,cosz,cosyand S: r→=u2,u,v, 0≤u≤1, 0≤v≤π2

Q: (vi) P= Q = (P(N); C), and o defined by {1} if 1 € U, {2} if 2 € U and 1 ¢ U, p(U) = otherwise.

A:

Q: in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1…

A: a) If 1 and 7 are adjacent then we consider 1,7 as one number.  It can be 17 or 71. 2 ways. When 1,7…

Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: 3. Let What is (CA) U B? (a) {x € Z] x % 4 = 2} \ {10} (b) {x€N | x % 4 = 2} \ {10} (c) {x€N |…

A: Using the way in which the sets are defined we solve the problem. The typeset solution in latex is…

Q: (2) Let S := {1,..., n}. Compute the number of towers of length of the form A1 c A2 c S, where A1 +…

A: A tower of length  set is a basically chain of subsets of different size.

Q: Suppose you are given that A, B, C, D, E, F are points satisfying A ∗ B ∗ C, D ∗ E ∗ F, AB ≅ DE, and…

A: To go further, keep the axioms and propositions of incidence betweenness geometry handy...…

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: 14. Let A = {r € R : 2 < z < 4} and B = {r €R: -4 <I<1}. Prove that |A| = |B|.

A: