Let ∼be the equivalence relation on R defined by x∼y if and only if ⌊x⌋=⌊y⌋. Using interval notation, describe the equivalence class of 15

Q: - Recall that for x, y € R, x - y = R is the absolute value of x-y. That is, if x-y 20 if x-y<0. x-y…

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

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Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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Q: Show that if both f: A ---> B and g: B ----> C are bijective, then g 0 f: A ---> C is bijective.

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Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

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Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: d) S₁²=1 sin³dz

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Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: Please explain each property (withs #'s) Recall that for x, y ≤ R, |x - y ≤ R is the absolute value…

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Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: 1, Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6,} Such that aRb means a+2 <= b.…

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Q: 1 Let R= {(x,ex):xe R.n € Z}. (Here e = 2.71828... as usual.) Prove that R is an equivalence…

A: Given: R=x, enx : x∈ℝ, n∈ℤ. To Prove: R is an equivalence relation on the set of real numbers.

Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: = Give an example of an equivalence relation R on the set A {a, b, c, d, e, f, g, h} such that there…

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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