Consider the plane (P) related to x-axis and y-axis system. Let R be the binary relation on (P) defined by: М (х, у) R M'(x', у') х-у3х* - у' |(a) Prove that R is an equivalence relation on the set of points of (P). (b) Interprete geometrically the equivalence class of the point A (1, 2). (c) Describe geometrically the set (P)/R.

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

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

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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.

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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

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Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

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A: partial order means reflexive and antisymmetric.

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Q: Let R be a relation on Z. Then Ris an equivalence relation if it is defined by xRy if and only if…

A: R is an equivalent relation iff R is reflexive. R is symmetric. R is transitive.

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A: (x,y) ∈ R × R (x,y) ∈ C means    x2 + y2 =4

Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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Q: . Define a relation on R²\{(0,0)} by letting (x₁, y₁)~(x₂,Y₂) if there exists a nonzero real number…

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

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Q: Exercise 1 find the relation Ship between PeSIstarce IC furrent) from the table below, VAR 1 2-28 10…

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Q: (1) What is the relationshi etween lines 11 and 12? wl Y = 2 y = 1+ 2t Z = 1+t

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.