Given: AABC with A(1,6), B(5,4), C(5, –2) Prove: The circumcenter of AABC is E( 1, 1 )

Q: Show that the statement If n E N and a E Z*, then [Q(Va): = n is false.

A:

Q: 3. It has to: i = (2, –3,4); i = (-5,1,0); w = (4,2,1), perform the following operations: u+v; u-w,…

A:

Q: c. Compute P((BUC)n2). с. d. Compute P((An E)U 3). Compute P(ECn 4) е. f. Compute P((BU D)ºn1)

A: There are 245 couples in total  a) Number of couples who were married in 2000 and had 2 children is…

Q: Answer the following: Given: A = {

A: Given: A=1, 2, 3, 4, 5, 6B=2, 4, 5, 6C=1, 6, 7

Q: Prove the following: If ā and b are in R', then (5 -a)×(5 +a)=-2(āxb).

A: Given a⇀ and b⇀ are in R3. To prove :  b⇀-a⇀×b⇀+a⇀=-2a⇀×b⇀

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

A:

Q: EXERCISE 5.7.5. Let S := {n+2": ne Z}). Then Acc(S) = {-00, +00}. {0, +00). {-00,0, +00}. {-00,0).

A:

Q: Let Give the 2,1 entry of 4-¹. a) 0-¹ b) 0¹/2 c) 03/2 d) 0-5 e) 0-2 f) O None of the above. 02 2 A-1…

A:

Q: A.2 (b) Show that, in general, ßo ‡ Bo, and find in terms of Y;. In what particular case is ßo = Bo?…

A: Simple Linear Regression(SLR)          It is a statistical method that allows us to summarize and…

Q: 7. In ABCD, AC and BD divide each other in half at E. (a) Prove that ZDBC ZBDA. (b) Prove that ADBC…

A:

Q: If Σ P(x) = k2 – 8 then, the value of k is? a)     1   b)     Insufficient data   c)     0   d)…

A: P(x) is the probability of x taking certain values   As P(x) is the probability , the sum of the…

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

A:

Q: Let A ={ 2,3,4 } and B = { 5,1,7 }. Α) Find (Σα (Σb) B) Find Σa?b -1

A: Solution: From the given information,

Q: b) Compute Sc C 2z²+z+₁ dz, where Z² +4 iii) C = {z: \z+i)=2

A:

Q: Given n(U)=70​, n(A)=29​, n(B)=21​, and n(A ∩ B) =4​,  find (A∪B)'

A:

Q: 6. Give a direct proof of: (PV R) V (P→ Q), ¬(P → Q); R → (P → Q) → P

A: Introduction: A mathematical statement is proved naturally without constructing a truth table. The…

Q: 3. If U and V are such that u; ='x; – A, v; =y, - B, then Cov (U, V) is :

A:

Q: 2) find a general salation you t 4y! + CTT? +4)1 3D 2. B

A:

Q: - 1 Let A = 1 3 Find:- 5 a ) 2 A+ B' b) В'А' — I

A:

Q: Which of the following is not valid? p→q AP pvq B) -p (c) q-r p→r D) -p

A: We need to check which of the following is invalid.

Q: 9f a,b,c,d EN & a = b frod n) C=d(modn) sherw that bd(radn)

A:

Q: a) n(A) =    b) n(A∩B) =  c) n( B' ∩ C' ) =

A:

Q: 2) (n² – n – 29) ÷ (n – 6) 4) (k² – 7k + 10) ÷ (k – 1) tv

A:

Q: The formula for slope between two points (x1, y1) and (x2, y2) is: m = 5-4 O True O False

A:

Q: Question 1: Prove the following identifies: a) A-V AV.

A:

Q: 1.) god (+n₁ fn + 1) = 1 VAZI

A: Kindly note, as per the office rule, we are supposed to solve the first problem from a set of…

Q: .    Verify that: a)    (A - B) – C = A - (B ∪ C) b)    (A Δ B) ∩ B = B - A

A:

Q: Let​ n(U) = 40​, ​n(A ∪​ B)′ = 6​, and​ n(A) = 19​, find​ n(B –​ A).   ​n(B –​ A)

A:

Q: EXERCISE 5.7.1. Let S := {2": ne Z). Then Acc(S) = □0. {2": ne Z, n<0}. {0}. {0, +00}.

A:

Q: Given that P = () and Q: = () Then: P + Q =

A: solution is given below.

Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

A:

Q: O Prove thal P(m, n) - (n,m).

A:

Q: In (R, Tµ), if A = (1,3) n (Q – Z) then A = - %3D O a. [1,3] n (Q- Z) O b. R O c. [1,3] – {2} O d.…

A: Given that, In ℝ,ζυ, if A=1,3∩ℚ-ℤthen calculate the value of A.

Q: Campute the improper in hegnel S, xe

A:

Q: Yk+1 (1, 1) Ук FIGURE 2.11: yf+1 = Yk• %3D

A: See the attachment