Let . be the operation on the cartersian product of real numbers R • R such that (a,x) * (b.y) = (ab,x+y). Then the imverse of (a,x) is O E. None of the above.

Q: Let G= Z* and let * be an operation in a * b. Is a * b = ab/2 is closed under the operation?

A: Disproof by an example.

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A: Answere : The two example are given below :

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

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Q: let f={ Ca,b) : a,bGR 3 and +,. defined on F as (a,b) + ( Cd)- (arr, bod) vla,b).(c,d) Ef Pollous:…

A: f=a,b : a,b∈Rg:f→M2×2 defined asga,b=ab00 , ∀a,b∈F

Q: Let * be the operation on the cartersian product of real numbers R *R such that (a,x) * (b,y) =…

A: Given that, let * be the operation on the cartesian product of real numbers R*R  such that (a, x) *…

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Q: Let A, B, C, and D be sets.

A: First, (AxC)U(BXD) ⸦(AUC) x(BUD)Take left hand side first , let  (x,y) ∈(AxC) U(BxD)=&gt; (x,y)…

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A: The objective of the question check for inner product.

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Q: 10. Let X , j= 1,.., n, be i.i.d. r.v.'s such that E(X,)= µ, o'(X)=o', both finite. j' Show that E(X…

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Q: (b). Let Y = {a, e, o, i, u}, take two relations R and S on Y and Prove that (SoR)-1 : R-1os-1.

A: composition of relations

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Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: 7.39 If R = r - r' and R = R|, show that 1 R |3| R3 where V and V' are del operators with respect to…

A: To Show- If R = r - r' and R = R, show that ∇1R = -∇'1R = - RR3 where ∇ and ∇' are del operators…

Q: a, be R H I 's an ideal of R if and anly of a-beI. for then a+I b+I %3D

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Q: Let f,g,h: A→ A be any bijective functions. Then (fogoh)-1 f-1og1oh-1 h-1og-1of-1 O is equal to the…

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Q: 2. Let f : X → Y be onto. For each b e Y, let A, {As : b € Y} is a partition of X. f6]. Prove that

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Q: c If in is an involution of X, show that (r, y)" = (yi", xi") is an involution of X2). %3D

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Q: the set of real numbers R there is de fined as: 21 xy = 23 +y3 that (TR, x)is Abelian G Proye

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Q: Let * be the operation on the cartersian product of real numbers R* R such that Then the (а,х)*…

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Q: Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x E R | cx + d + 0}. The…

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Q: Let 9-(a: a€R}, then T is Borel algebra.

A: Clearly the measure of the set is =0 .

Q: uppose that X~N(µ, o²) and that P(X 3.6) = 0.6554, what are the alues of u and o?

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Q: Let J={(a,∞): a€R}, then T is Borel algebra. صواب İhi

A: True

Q: Suppose that for every r E R, pqr 0. Show that R is isomorphic to R/I, × R/Iq.

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Q: (18) (a) Prove that R* is isomorphic to R>0 x Z2. (b) Is Q* is isomorphic to Qo x Z2? Prove your…

A: a)  To prove :- ℝ*is isomorphic to ℝ&gt;0×ℤ2. Proof :- Define a map ϕ : ℝ&gt;0 ×ℤ2→ℝ* by…