I elements is A, then the

Q: Show that if ac|bc, then a|b.Show that if a|b and b|a then a=±b.

A:

Q: 2.7, 12 0.5, Let D = -9, 0, 2. Which elements of D are non-negative? (Select all that -6

A: A set is given by, D = -6, 5, 0, 27, 2.7, 122, 0.5, π. The objective is to find the non-negative…

Q: ieN (4 For each nEN, let A, = {-2n,0,2n}. (a) UA; = (b) NA: = ieN ieN

A:

Q: m and n, mn, such that: and U(m) ~U(n). Find integers a) |U(m)| = |U(n) b) |U (m)| = |U(n) and U(m)…

A:

Q: 2. Let ū = (-1, 2, –1) and i = (-2, 0, 3). Find ū · ū.

A: Apply dot product

Q: Prove let B= 6+ I %3D : m = ',2,3, 3m S. Then inf(8) =6

A:

Q: Given: VP Construct: VW such that VW = 4. VP V

A: Given: vp vw=4 vp

Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: estion 2. Prove that if AUB= A is true, then AnB = B is also true, AND CONVERSELY.

A:

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

A:

Q: 2) Let R be aring. An element a6 R is called a Zevo divisor if there exists beR such that a) a.b =o…

A:

Q: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

A: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

Q: I, \B|, A + B, and |A + B|. Then verify -1 1 8. 1 0 1 A = 0 1 1 B = -1 1 8 1 1 -1 0 1 8

A: Given: A=-11801111-1, B=101-118018

Q: Which of the following are con. and which div.? 1.{ 2

A:

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: Prove or disproe: If C is a groun and a hsC then (ab)-1 h-1a-1

A:

Q: Example 38.18. Prove that (a) div A, = VgA)

A:

Q: Let A = (-0,0), B=(0,0) then AUB=

A:

Q: Example Let A= B = 1. proof |A x B| = |A| × |B| %3D

A: Solve individually left hand side and right hand side expression to prove the given expression.

Q: If n quantities a, b, c, . . . . k are in A.P., then 1 + +....+ is b c 1 - - k 2n 2n (a) a + k (c)…

A:

Q: 5. The set P = {a + bi|0 ≤ a < 1,0 ≤ b ≤ 1}

A: (6) Closure P¯  of P is the smallest closed set containing P. Given, P=a+bi | 0≤a&lt;1 , 0≤b≤1

Q: CI/ let A= {1,2}, B={2,4,6}, R: A? =B, then find R

A: Given: A = {1, 2} ,    B = {2, 4, 6} Now define the relation:  R = {(a, b) : A2 = B }

Q: (a) Show that if (a,342) = 171 and (b, 342) = 171 then (a+b,342) = 342. %3D %3D (b) Show that if (a,…

A:

Q: [AB, C] = A[B, C] + [A, C|B (Proof that)

A: simply &amp; expand each one we get. [AB, C] = ABC - CABA[B,C] = A(BC - CB) = ABC - ACB[A,C]B = (AC…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

A:

Q: Givien the following defintion  U={1,2,3,4,5, 6,7} A={1, 2,4,5} B={1,3,5,7} How many elements are in…

A: Given:U={1,2,3,4,5, 6,7}A={1, 2,4,5}

Q: Example: Debem in e the principle Value of the argumint Solution.

A:

Q: an = an -a t an -z and a,=3,az =9 az= as =

A: Given :

Q: P(1,1, 1) Q(-1,1,1) R (0,0,4) Datcrmine an cquation of the planc II in IR that contains P.Q and R

A:

Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

Q: II. Prove/Disprove: 1. (¬A → → ¬B) + (¬C A A) = ¬ (A V –¬B) + (В — С)

A: We will check whether the given statement is equivalent or not.

Q: Let X = {a, b, c, d} , T = {0, X, {a, b}, {c, d}}. (a) Is B = {X, {a,b}} base for (X, T)? Why? (b)…

A: a) By definetion of basis for a topology, it is family of open subset of X such that every open set…

Q: A,B and C such al numbers x and

A:

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

A:

Q: 5. Write a proof. Given: ZE = ZH ZHFG = ZEGF Prove: AEGF= AHFG G

A: We will prove the following.

Q: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

A:

Q: (4) 9Afi - fiAgi (a) Show that A 9i 9i+1

A:

Q: 1. Let A = {a, b, c}, B = {x, z}, and C = {0, -1}. Find а) В хАх С. b) С х Вx А. с) С хАх В. d) В x…

A:

Q: Let ū = (1,– 3,2), v = (2, 2,1) , w = (- 4, -1,2), find the following or state it doesn't exist or…

A: “Since you have asked multiple questions in a single request, we will be answering only the two…

Q: [1 2] If A = then show that |24|=4||| %3D 4 2

A: Introduction :We have given a 2*2 matrix A. We have asked to show that |2A| = 4|A|.

Q: Let 9= {[a,b]: a,bER}, then 9 is Borel algebra

A: TRUE ;

Q: (a-b) if a,b,c,d are in continued properties,prove that a (b-c) d

A:

Q: 6. No : o Show that sa= (Q-1)a

A: To show :- ∆ ax = a-1 ax

Q: Let A = 1 2 1 and v = If the entries of A and v belong to Z3, what is the third entry of Av? Answer:

A:

Q: II. Prove/Disprove: 1. (¬A → ¬B) Ð (¬C ^ A) = ¬(A v ¬B) →¬(B –→ C)

A: Solve the Expression using boolean algebra   ¬a⇒¬b=a∨¬b(a∧¬c)⊕(¬a⇒¬b)=(a∧c)∨(¬a∧¬b) Also, the…

Q: ercise 5.1 Show that if Q-x, then E[QI = r and var [Q] = 2r. Hint: Use the representation Q = E", Z?…

A: Distribution in statistics or probability is the shape in which the data behave when plotted. There…

Q: discrete math

A: We are entitled to solve one question at a time so i am providing solution for first question ,…

Q: 4. Prove: Let a, b e Z*. If a|b and bla, then a = b or a = -b.

A: If a/b and b/a then prove that a=b , a=-b.

Q: Given u = (-4,7) and v = (5,2), compute the following. Give your answer in the form . a. u + v =| b.…

A: