For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti- symmetric, or neither; transitive or not transitive; a. For x, y E R, xFy if x > y

Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

A:

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: For Exercise, a relation in x and y is given. Determine if the relation defines y as a one-to-one…

A: A relation f is one -to -one , if no two elements in domain of f corresponds to the same element in…

Q: Let A = {2, 3, 4} and B = {6, 8, 10} and define a relation R from A to B as follows: For every (х,…

A: Relation R is defined as:

Q: A (a,b,c,d} 1. Find a relation which is symmetric but nelther reflexive and not transitive on A. ii.…

A: A relation R from a set A to another set B is reflexive if and only if x R x holds for all x in A. A…

Q: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than…

A: That's easy. Have a great day!!!

Q: Given the relations F = {(q, p)|5p2 − 4q − 2 = 0 p, q ∈ ℝ} and                                    G…

A: For function of two variables y=f(x), the set of all values of x for which y is defined is called…

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

A:

Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

A:

Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

A:

Q: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

A:

Q: . Define a relation from Z to Z as follows: For all x EZ and all y E Z, x and y are related iff y =…

A:

Q: For each relation, declde whether or not It Is a function. Relation 1 Relation 2 Domaln Range Domaln…

A: A relation is said to be a function when there is a unique image for every preimage.

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: Let A = {0,1, 2}. Each of the statements below defines a relation R on A by (m,n) E R if the…

A: A relation between two sets is a set of ordered pairs x,y where x is an element from the first set…

Q: Given the relations F = {(q, p)|5p − 4q2 − 3 = 0 p, q ∈ ℝ} and                                G =…

A: Given relations are  F=q,p:5p-4q2-3=0 , p,q∈ℝ        (i)F=p,q:5p-4q2-3=0 , p,q∈ℝ        (ii) Let,…

Q: 1 Complete the second and third columns of the table. Where possible, complete the last column as…

A: We have a table, we have to fill in the blanks in the table.

Q: List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b) e…

A:

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

A:

Q: Consider the recurrent relation An = 2 An-1 - 3 and Ao = 2, n 1 %3D Then A2 equals O a. 1 b. 10 Oc.5…

A: Recurrence Relation:  A Recurrence Relation is an equation that defines a sequence based on a rule…

Q: Given the following relations on the set of real numbers, find R O S: R= {(a, b) E R² | a < b}, the…

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

Q: The domain of a relation R is the set of integers. x is related to y under relation R if x 2 = y.…

A:

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

A: Given: The number of watermelons in a truck all are weighted on a scale. The scale rounds the weight…

Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

A:

Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: To find- For each relation, indicate whether the relation is: Reflexive, anti-reflexive, or neither…

Q: Find the first 5 terms of the recurrent relation below. An = 2An-1 + 3An-2 where n ≥ 1, and A0 = 1…

A: Using simple calculation

Q: Which of the following relations is an equivalence relation? [A] xRy if and only if x-y=8 [B] xRy if…

A: We have to find which relation is equivalence relation.

Q: Directions: Identify the domain for each relation using the set builder notation. 1. y 5x-4 6. g(x)…

A: Given equation of the function is: y = 5x - 4

Q: Je fine a binary relation Rond by R= [(y)] ER² x ус

A: Given is : R={(x,y)}∈R2:x-y∈Q We have to show that it is an equivalence relation.

Q: 1. State the domain of this relation. * 2 -2 {x ɛR} O {x ɛ R, x + 1} O {y ɛ R} O {y ɛ R, x + 1}

A:

Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

A:

Q: Match the ordered pairs of integers on the left with the relation they belong to on the right.

A:

Q: equivalence relation

A:

Q: Suppose that the relation H is defined as follow. H=(7,7),(0,-1),(3,9),(-9,3). Give rhe domain and…

A:

Q: Given the relation in the diagram determine x such that f(x) = -2 5- 3+ 1+ -5 -4 -3 -2 -11. 1 2 3 4…

A:

Q: List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b) e…

A: Given A={0,1,2,3,4} and B={0,1,2,3}

Q: For each of the following relations, give the domain and range, and indicate which are…

A: Given, relation is 3, 5, 5, 7, 7, 3. Domain is the set of x values for which function is defined. In…

Q: Give an example of a relation which is a) One-one and onto b) Many - one and onto c) One-one and…

A:

Q: Coot R be the relation A = S 2, 34 S,,73 de fned the ゲ rule Cab) ER if the wlese Carbs dixindle the…

A:

Q: If an expoential relation such as y=bx, if b > 0 and b ≠ 1, then the y intercept is at zero. Is this…

A: The given problem is to check whether the y intercept is at zero is true or false.

Q: For Exercise, a relation in x and y is given. Determine if the relation defines y as a one-to-one…

A: Here, a relation R between the two sets is shown. Suppose 1st set is X and 2nd is Y. Thus, X= {2, 3,…

Q: Let A= B = Z. Let R be the relation from A to B defined by a Rb if and only if a² – b² = 9.…

A:

Q: Determine the domain and range of the relation R defined byR = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4,…

A: We make a table for the relation x x+5 0 5 1 6 2 7 3 8 4 9 5 10

Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: (a) Take x =1.

Q: The following ordered pairs (z, y) define the relation Q. Q= {(-1,4), (-2, 3), (4, 4), (2, – 2)} Is…

A: Given relation is  Q=−1,4,−2,3,4,4,2,−2

Q: 1. Determine if the relation defines y as a function of x. AAA a. -3-2-1 b.

A:

Q: Give an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii)…

A: i. Symmetric but neither reflexive nor transitive.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.