Let f=​{(−2​,1​),(1​,−1​)} and g=​{(−2​,−4​),(2​,−1​),(5​,6​)}.   Find f•g and its domain. What is the​ domain?   ​(Use a comma to separate your​ answers.)   f•g= ​(Type an ordered pair. Use a comma to seperate your answers)

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b): a < b?.…

A:

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: The relation R on X={1,2,3,4}defined by (x,y) € R if x=y.

A:

Q: List the members of the set A={x| x is a real number such that x2=1}, separating them by a comma.

A: Set A contains all real number x such that x2 =1

Q: Let A = {1, 2, 3, 4} and let f:A ->A be defined as {(1, 3), (2, 4), (3, 1), (4, 3)}. Is f…

A:

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: Reflexivity: Since x≠x+2 , therefore, (x,x)∉R and hence R is not reflexive.   Symmetricity: Let…

Q: Let x={1,2,3,4} and y={1,2,3,4,5,6,7,8,9,10}   and "f" from X to Y is given by…

A:

Q: Describe the domain and range of the function. f(x, y) %3D 8x2 - у Domain: o {x, v): v 2 0} {r, o…

A:

Q: Let R be the relation defined by x R y =x<y° Determine if R is an order relation on N? on Z? Justify…

A:

Q: Check whelher z[Fs] is a Euclidean domain?

A:

Q: Let f : {1, 2, 3} → {a, b, c} be one-one and onto function given by f(1) = a,   f(2) = b and f(3) =…

A: Consider

Q: Let R be defined on A x A where R = {(1, 1), (1, 2), (2, 3), (3, 2), (3, 3)} State a counterexample…

A: Given that    R= { (1,1),(1,2),(2,3),(3,2),(3,3) }we have to show that .... (a) R is not relaxive.…

Q: 4. Show whether or not f is bijective. Letf : R → R_be defined as f(x) = I피+1 %3D

A: A function f is said to bijective if it is one-one and onto

Q: Assume (r1, y1) ~ (x2, Y2) → f(x1,Y1) = f(x2, Y2). Prove that ~ an equivalence relation.

A:

Q: Check whether Ris reflexive, symmetric or transitive and hence determine whether the relation Ris…

A:

Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

A:

Q: Let f, g,h: A→ A be any bijective functions. Then (f ogoh)-

A:

Q: Let f,g,h: A A be any bijective functions. Then (f ogoh)-1

A:

Q: 2. Consider the function ƒ : R × R –→R x R defined by Determine the powers of f. (Note that R × R…

A:

Q: Let A and B be set .Show that AxB → BxA Such that (a,b)=(b,a) is bijective function

A: A function f from a non-empty set A to anther non-empty set B is said to be an one-to-one or…

Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

Q: Let R be the relation on Z given by R= {(a,b) : a < b}. %3D (a) Find R-1. (b) Find R which is Z x Z…

A: relation on Z.

Q: Find a function f and a real number a such that

A:

Q: Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈…

A:

Q: Let R denote the set of real numbers. Let f: Rx R-> R x R be a bijective function defined by f(x, y)…

A: Given a function  f: R x R -&gt; R x R such that f(x, y) = (x + y, x-y)

Q: Let R be the set of real numbers and f: R-(1} R-{3} be the bijective Then f-1(x) is 3x function…

A:

Q: Define the relation A=((x,x+ 1):xER] Show that A, is a function from R to R.

A:

Q: c) Let f: A B and g: B → C be surjective functions. Prove or disprove whether gof is surjective.

A: See the attachment

Q: Questron 5. Check whether the relation R in R defined by R = {(a, b): a < b³} is reflexive,…

A:

Q: Let f, g,h: A A be any bijective functions. Then (f ogoh)-1 h-1 og-1of-1 Ois equal to the above None…

A: Given that                     f,g,h:A→A be any bijective functions. Then we have to find the…

Q: Let A- {#, 7, x} and let R be the relation on. A given by R {(7, 7). (#, #)}. Prove or disprove…

A: Transitivity is a property of verbs that relates to whether a verb can take objects and how many…

Q: Let R denote the set of real numbers. Let f: Rx R-> Rx R be a bijective function defined by f(x, y)…

A: Introduction :

Q: Prove or disprove whether the function f (r) = a +2 is a bijection from R R %3D

A:

Q: Let X = (a, b, o} and Y = {1, 2, 3, 4}. Define a funotion from X to Y by the arrow diagram below %3D…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Let f, g and h be functions from R to R. Show that(f + g) oh = foh + goh(f . g) oh = (foh) . (goh)

A: To prove:

Q: Define a relation P from R to R as follows.for all real numbers X and Y with X>0 (X,Y)€P means that…

A:

Q: Let A and B be sets. Show that               f : A × B → B × A such that                  f(a, b) =…

A: Given:

Q: The relation R on set A = {0, 1, 2, 3, 4, 5} is given by R = {(0, 0), (0, 1), (0, 5)(1,0),(1, 1),…

A:

Q: Let ℝ denote the set of real numbers, and  β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which…

A: The given relation β⊂ℝ2 is: β=x,y∈ℝ×ℝ | xy≥0 The properties of a relation is: Reflexive Irreflexive…

Q: Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive andtransitive but not…

A: Given, the relation R in R defined as R = {(a, b) : a ≤ b}.

Q: 6. Give an example of a relation Ron A {-1,-3, -5} such that: (a) Ris both symmetric and…

A:

Q: Exercise 1. Let R be the set of real numbers and f: R-(0}→R-{1} be the bijective function defined by…

A:

Q: Prove that dual space of R^n is R^n( its Functional analysis topic)

A: to prove dual space of ℝn is ℝn. proof let the dual space of ℝn be denoted as ℝn*=M we will show…

Q: a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Give an example of (v1, V2, V3) and (W1, w2, W3) independent se- span(wi, w2, w3) and {v1, v2, v3}(…

A:

Q: Let f be the function from (a, b, c, d) to (1, 2, 3, 4) with f (a) = 4, f (b) = 2, f (c) = 1, and f…

A: Consider a function f:a,b,c,d→1,2,3,4 with fa=4, fb=2, fc=1 and fd=3. A function is a bijection if…