Let A be the set of all lines in the plane. Consider the relation a ~b if and only if line a is perpendicular to line b. Is this relation reflexive? True False

Q: The set of all directed line segments that are equivalent to a given directed line segment PQ\is…

A: The set of all directed line segments that are equivalent to a given directed line segment PQ \ is a…

Q: Let A be the set of all triangles defined by R = {(A1, A2) : A1 =A2). Show that R is an equivalence…

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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: Show that the relation R on a set A is symmetric if and only if R = R-, where R is the inverse…

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Q: ist the ordered pairs in the relation R from A = 0, 1,2, 3, 4, B = 1,2, 3, 4, 5, where Ris defined…

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Q: . Define a relation R from R to R as follows: For every (x, y) ERX R, (x, y) E R means that y = r.…

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Q: Define a relation C rom R to R as follows: For any (x, y) ERXR, (x,y) E C means that x2 + y2 = 4.…

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Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: Does the relation "is perpendicular to" have a reflexive property! Yes No Does the relation "is…

A: reflexive property of perpendicular line means that a line is perpendicular to itself : but this is…

Q: Show without using the Heine-Borel theorem that the line R is not a compact set in R ^ 2

A: The proof is done using the definition of compact set. A set S is said to be compact if and only if…

Q: Determine the image of the line Im (z) = -2 under the mapping f(z)3Di(z) and describe it in words.

A: Given Imz=−2 and a mapping fz=iz¯2 We know that z=x+iy Since, Imz=−2 Hence, y=-2 Now,…

Q: Prove the theorem 2.6.3 "if l is any line, then there exist at least one point P such that P does…

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Q: Let L be the set of all lines in XY plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: Line L is parallel to itself. This means L is parallel to L.So, (L,L)∈RSo, R is reflexive.

Q: Consider the line segments[1,2] ={x∈R|1≤x≤2} and [0,3] ={x∈R|0≤x≤3}. Show that[1,2]and[0,3]are…

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Q: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

A: Topic = function

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: Identify the relations which are also functiuon: Ox = y? Ox+y= 1 O a? = y? %3D Oy = a?

A: X+Y =1  This relation is also a function because for every x there is an unique image, y. X^2=Y^2…

Q: Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point,…

A: Axioms3 of Fano’s geometry: The axiom 3 in Fano’s geometry is stated as “not all points of the…

Q: Let L be the set of all lines in a plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: The given relation R is defined as follows.

Q: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

A: Relation

Q: Determine the image of the line Im(z)= -2 under the mapping f(z)= i(z ) and describe it in words.

A: Im(z)=-2 represents a straight line y=-2let z=x-2i where x is real number. ⇒u+iv=f(z)=iz2=ix+2i2…

Q: Prove that if two nonvertical lines have slopes whose product is - 1, then the lines are…

A: As we are given that the product of slopes is -1let l1 be the first non-vertical line having slope…

Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: Let r = ⟨x, y, z⟩ and r0 = ⟨1, 1, 1⟩. Describe the set of all points (x, y, z) such that r − r0 =…

A: Given: r=x,y,z and r0=1,1,1 To describe the set of all points x,y,z such that r-r0=2 Solution:…

Q: Define a relation C from R to R as follows: For any (x, y)  £ R x R.  (x, y)  C means that x² + y²…

A: Given: Define a relation C from R to R as follows,for any (x,y)∈R×R (x,y) C means that x2+y2=4

Q: Assume that all lines that appear tar 1. Find AB

A: We can find the length of AB in the following step

Q: Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or…

A: The given relation R is defined as follows.

Q: let A = {1, 2, 3, 4, 5}. Determine whether the relation R whose digraph is given is reflexive,…

A: The relation is reflexive if (a,a)∈R, ∀a∈R. The given digraph is not reflexive such as 1 is there in…

Q: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive relation

Q: Let : [0, 1] → [0.c], te- and let w be a 1-form on R. What and foe, and why? is the relation between…

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Q: Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is…

A: Given, Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) :…

Q: 3. Define a relation S from R to R as follows: For all (x, y) e R xR, (x, y) eS means that x2 y. a.…

A: Given x,y∈S  Mean x≥y    x,y∈R×R

Q: Define a relation R from R to R as follows. For every (x, y) ERXR, (x, y) ER means that y = x. (a)…

A: Given a relation R from R to  defined as  For every x,y∈R×R,x,y∈R means that y=x2 (a) We have to…

Q: Does the relation "is perpendicular to" have a reflexive prop- erty (consider line €)? A symmetric…

A: A relation R is said to be reflexive if is related to itself that is aRa, relation R is said to be…

Q: Prove that if the slopes of two nonvertical lines are negative reciprocals of each other, then the…

A: let's slope of a nonvertical line is m then slope of another nonvertical line will be -1m as slope…

Q: List the ordered pairs in the relation R from A=0,1,2,3,4, B= 1,2,3, 4, 5, where Ris defined as (a,…

A: Given sets are: A={0,1,2,3,4} B={1,2,3,4,5} Relation R consist of those ordered pairs (a,b) such…

Q: A relation R is called circular if (a, b) E R and (b, c) e R implies that (c, a) e R. Show that a…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve the…

Q: b) On the set L of all straight lines into the plane, we define a relation R as follows: 1, R1, if…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing the same.…

Q: Define a relation S from R to R as follows: For every (x, y) ER X R, (x, y) E S means that x> y. a.…

A: (a)It is given that the relation S from R to R is defined as for every (x, y) ϵ R × R, (x, y) ϵ S…

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: Is anyone of the veetors e. 2-, ERa linear combination of the others? If so, find the relation(s)…

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Q: Prove that in the hyperbolic plane, given a positive integer n there exist n + 1 lines such that…

A: In the hyperbolic plane, given a positive integer n there exist n+1 lines such that earth sit of n…

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: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

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Q: Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the…

A: It is given that, the distance of point P from the origin is same as that of distance of point Q…

Q: Define a relation S from R to R as follows. For every (x, y) ERXR, (x, y) e S means that x 2 y. (a)…

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Q: Sketch the set of all points (x, y) such that x + y| < e*.

A: Consider the function x+y≤ex. An absolute function is defined as x=x if x≥0-x if x&lt;0. So, there…

Q: Let l: = = -: - 5 and p = (1,7, -4) + A(1, -2, 2) be two lines in space.

A: