5. In the table, indicate if the expression is: 1) a function, 2) onto, 3) one-to-one, and 4) bijective. Is this.. a function? one-to-one? onto? bijective? S:R→R; S(2) = |z| yes / no yes / no yes / z yes / no {(1,a), (2, c), (1, 6), (3, 6), (4, 4)} yes / no yes / no yes / no yes / no S:R→ R; S(z) = 5z +7 yes / no yes / no yes / no ye / no 5:R' → R; S(z) = vVE ye / no yes / no yes / no yes

Q: if and only if F-1: R(F) →X is bounded.

A:

Q: 2 Let F be a closed set for k = 1, 2, ... , n in (S, d). Show that |J F, is closed. k=1

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

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: 4. Let f : R –→ R be defined by f(x) = 2x +3. (i) Show that f is 1-1. (ii) Show that ƒ is onto.…

A: As per guideline we are supposed to answer only first three subparts of the question. The solution…

Q: Determine the global extreme values of the function on the given set without using calculus f(x, y)…

A:

Q: Fuppose that the relation R indicates whether c articular student is registered for a particular c…

A: In this question, the concept of Relation is applied. Relation The relation is a relationship…

Q: 7 (:) Prove that f(x) : is convex.

A: Given the function f:ℝ→ℝ2 by, f(x)=xs Note that the domain of the function f(x) is convex.

Q: Consider two sets, A = {1, 2, 3, ..., 100} and B = {3, 5, 7, 9, ... , 201}. Prove that |A| = |B| by…

A:

Q: 15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Q#2. Give an explicit formula for a function from the set of integers to the set of positive…

A: Function: Let A and B be two non empty sets. If there exist a rule f which associates to every…

Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: 2. (a) Assume that (a, b) is a bounded open interval in R. Using Mean Value Theorem, prove that if…

A: We will use MVT.

Q: 1. Let Y = (0, 1, 2) and Z = (0, 1) and define as relation R from A to B as follows: Given any (x,…

A: (NOTE- The relation R should be from Y to Z instead of A to B.) Given sets are, Y=0,1,2 and Z=0,1…

Q: Give an example of onto but not 1-1 function f: 7⁰ → Z>⁰. tit 11-C.

A:

Q: Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric?

A:

Q: (5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove…

A: In 2 nd part construct a function

Q: (a) Show that the formula (VæR(g(x), x) = Vx3yR(y,x)) is universally valid, where g is a 1-place…

A: Part(a): As we know, ∀xRgx,x⇒∀x∃yRy,x Where g is a two place function symbol and R is a two place…

Q: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³

A: See the solution.

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

A:

Q: Let f(z) be an ODD fanetion. If the point (2,3) belongu to f, then another point likely to (0,0) (2,…

A: Given f(x) is odd function.

Q: Let Y = {0, 1,2} and Z = {0, 1} and define a relation R from A to B as follows: Given any {x,…

A:

Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )…

A:

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

A:

Q: 7. Find a counterexample or a proof for the following statement: If f: A- B and g : B- C are…

A:

Q: 2. Consider the relation on the natural numbers N defined as follows: for all x, y e N, xRy if and…

A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

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: Let g be the function defined by g(z) = |2| + 2|1- z What is the absolute minimum value of gon the…

A: The function,g(x)=x+21-x

Q: 2: A necessary condition for a function to be unimodal on the interval [a, b] is that strictly…

A: Statement: A necessary condition for a function to be a unimodal on the interval [a,b] is that…

Q: 4. Give an example of a function from N to N that is (a) one-to-one but not onto. (b) onto but not…

A:

Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

Q: Given x = {5,10,15,20,25,30} and y function from X to Y. Let f(5) = 400, f(10) = 100, f(15) = 500, f…

A: x=5, 10, 15, 20, 25, 30  &amp;  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: 11. Define a relation P from R to R as follows: For all real numbers x and y with x>0, (x, y)e P…

A:

Q: Let f(x, y) = domain of f is the set D = {(x, y)|x² + y² > 1}. Select one: 1 1 - x² - y² True O…

A: Given.

Q: (a) Show (a, b) ∼ R for any interval (a, b). (b) Show that an unbounded interval like (a,∞) = {x : x…

A: Let          (a, b)⊂R                        be an open interval.   So,         We define a function…

Q: Define a function g(x) of a random 1; if x2x, 0; otherwise variables by g(x) = %3D Where x, is a…

A:

Q: Let S = {0,1}. Exhibit all functions S → S and classify them as injective, surjective, bijective, or…

A:

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

A:

Q: Suppose you have the following relation: R: A-A where A = (a, b, c, d, e) %3D R= ( (a, b), (a, e),…

A: Given relation is R:A-&gt;A where A={a,b,c,d,e}R={(a,b)  , (a,e) , (b,e) }determine whether it is…

Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: LeA R be the relation defined the se4 Nx Z that (xy)EIC on so if and only if a) What is. the domain…

A:

Q: 21. The interval for function 13y-71 4 is (1,11/3) O[1,11/3] (-00,1)u(00,11/3) 0[1,11/3)

A:

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…

A: "

Q: Verify that the hypothesis of Rolle’s Theorem are satisfied. Then, find all numbers c that satisfy…

A:

Q: Let S be some non-empty collection of real numbers. We know that Vx E S, 3y E S such that x2 y.…

A: In this type of question you need to assume the set of x,y and S that satisfy the condition given in…

Q: 7.1.6 For the relation R = {(x, y) : x < y} defined on N, what is R-1, and what is the intersection…

A: The detailed solution is as follows below:

Q: Determine whether the following relation is a function from R into R. A Iso deter- mine whether that…

A:

Q: 3 10. Prove the function f : R- {1}- R-{1} defined by f(x) = ()° is bijective. %3D |

A: Given that the function f:ℝ-1→ℝ-1 is defined by fx=x+1x-13

Q: Consider f : X →Y, with domain X = {c,j,v, m, e, s, n, q, u, d, i, g} and codomain Y = {80,08, 57,…

A: SOLUTION-

Q: (a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is f one-to-one? Is f onto? Justify your…

A: