Show that ∗ : R × R → R given by           a ∗ b → a + 2b is not associative.

Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

A: Given problem:-

Q: Let J={a: aER}, then I is Borel algebra.

A: False Statement' Detailed Explanation

Q: Prove that if a, b e Z – {0}, then gcd(a, b) = gcd(a, -b)

A: Solution:-   gcd a,b= Greatest common divisor of  a  and  b ∗Every integer  that divides  a  and  b…

Q: What is eh REF of B? 1 2 1 1 B = نه who 1 0 -1 به T NC vсы N 5 0 2]

A:

Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: To the recipient, the following commendation is given in its standard form max z = Ax1 +B x2 A=6…

A:

Q: Need prove If R is a UFD and f(x) , g(x) are elements of R[x] , then c(fg) = c(f)c(g)

A:

Q: . Use the ideas from our study of product measures to prove the follow- ing. Let a j,k > 0 for j, k…

A: Take two conditions and expand the sigma ∑j=1 ∞∑k=1∞aj,k=∑j=1 ∞aj,1+aj,2+aj,3+aj,4+    ....+aj,∞ Now…

Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: 1. CHAIN OF REASONING: F= -E-R -S E → W RvS WV-S

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

Q: Prove R is irreflexive iff R ∩ idA = ∅. If idA={ ∈ A x A |a=b}

A: In the given question we have to prove that a relation R defined on a set A is said to be…

Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

Q: +(X+Z) = (X+ D DE Morgar Associativ O Distributive O Commutat .... is also

A: We will solve the problem.

Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

Q: If x=y+qp and f=xy+qp² Express x in terms of q,p and f

A:

Q: Let A = {x E R : 2 < x < 3} and B = {r €R: -1<r< 2}. Prove that |A| = |B|.

A: To prove this result we first show a objective map from [-1,2] to [2,3]. Then (2,3) is uncountable…

Q: Prove that ifx > 3 and y> 4, then xy > 11.

A:

Q: Let X and Y be defined as follows: X = {a E Z | a = 3x for some x E Z}, and Y = {b E Z |b = 3y – 3…

A:

Q: Determine the value of c so that the pmf of X is valid. 2 cx :-1, 1 P(X) = { c (x + 1), x = 0,2

A: Answer - Given PMF of X                 P(X)  = cx2x= -1, 1c(x +1)x = 0, 2 Find the value of c

Q: Prove that if A, B ϵ Mnxn(F) are similar, then det{A) = det(B).

A: Given:  A, B ∈ MnxnF are similar To prove:  det(A)=det(B).

Q: let (X, Z) %3. üit piece wise comnected ?

A:

Q: 2 Let A = then det(3AT) - 18 -6 -2 II

A:

Q: b) Prove that if x <y and z<w, then x+z<y+w.

A: Given: Suppose x&lt;y and z≤w. To prove: x+z&lt;y+w.

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: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

A:

Q: 3. Choose whether the following statements are true or false: (a) Ax.ly.y x is a-equivalent to…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: (b) Prove that the multiplicative inverse law is false for S. [That is, don't just write down a…

A:

Q: If X ∼ N (μX , σ2X ) and Y ∼ N (μY , σ2Y ) are independent, then prove X + Y ∼ N (μX + μY , σ2X +…

A: X~Nμx,σx2 and Y~Nμy,σy2 are independent. Here, X~Nμx,σx2. In this context, it is known that the…

Q: Prove: (i) b (A) CA if and only if A is closed. (ii) b(A) n A 9 if and only if A is open. (li1) b(A)…

A:

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: 1. Evaluate JJ (2². R where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 2}. (2x + y) dA

A:

Q: Determine what rule of replacement was used: (E ɔ F) · (G ɔ H) .: (E ɔ F). (~~ H ɔ ~ G) A Material…

A:

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: Show that the following argument is invalid: 3XF(x) V VyH(y),Vw(H(w) - S(w)) E3y-H(y)

A: The first expression is ∃xFx∨∀yHy. That is this expression states that there exists x such that F(x)…

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: Supposernc N and n 4 0 Then show that rn is positive if and only if r is positive

A:

Q: Show that (t As) can be derived from the premises pq, q→~r,r, pV (t As).

A:

Q: If C = {x:x² + 11x + 30 = 0, x ∈ N}, then C is a/an ?

A:

Q: In the diagram below, A ABC = AXYZ. C z- A Which statement must be true? O ZA ZX O ZC E ZY O AC YZ O…

A: Given data: ∆ABC≅∆XYZ We know that if two triangle are congruent then their corresponding sides and…

Q: The dual of (xỹ +(x + 1)) * (0 +yx)) is ((x +y)x * 0)) +(1* (y +x)). O True O False

A:

Q: Disprove the statement by giving counterexamples If m,n ∈ R, then |m + n| = |m| + |n|.

A: The equation is m+n=m+n.

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: -x+y<y. 2 If x < y, prove that x <

A:

Q: prove that for operatrs a and b which comute with thier commuters[a,b]=c,so that [a,c}=[b,c}=0 ,…

A: We know that ekABe-kA=B+kA,B+k22!A,A,B+... Given that A and B commute with their commutator then…

Q: Prove that B (xX+1; y ) + B (x,y+1)=B (X,Y) let П (х+1) = ХГ (Х)

A: We have the formula for beta function interms of gamma function is that B(m,n)=Γ(m)Γ(n)Γ(m+n)As we…

Q: Let A EMn (R) be given. If 11x11 = 11yll = 1 and x •y = 1, show that x=y

A:

Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.