Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine whether R is an equivalence relation or not.

Q: equations for the cost of a pizza at restaurants are shown below, where C presents the cost in…

A: Given that: The equation for the cost of a pizza at a restaurant are shown below, where “C”…

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

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Q: Define the relation R = {(a.b): a + b < ab} = A x B with A = {1,2,4} and B = {2,5,6). List all the…

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Q: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

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Q: Let Y be a relation defined by a Y b iff a times b is even. Is 5 Y 7 true?

A: Here, the given problem is on relation on set. We will solved the problem  step by step.

Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: Let ℝ+ denote the set of positive real numbers. Define a relation E on ℝ+ as follows: a E b  if and…

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Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Define a relation R on the set of all integers Z as follows: for all integers m and n, m R n → m = n…

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Q: Let A = {3, 4, 5}, and B = {−5, -3, -2, -1}. Define a relation R from A to B as follows: For all (x,…

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Q: Draw the diagraph of the relation R, where the relation R on {1,2,3,4} defined by (x,y) ∊ R if x^2…

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Q: Suppose that the relation R is reflexive. Show that R* is reflexive.

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Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

Q: A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference…

A: The difference between x and y is odd That is possible for  1-4=-3 1-6=-5 2-9=-7 3-4=-1 3-6=-3 5-4=1…

Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

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Q: Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y…

A: The given relation is: R=x,y| xy&gt;0, x,y are integers We know that a relation R on a set X is an…

Q: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

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: State whether the statement is true or false : '' All relations are mapping but the converse is not…

A: we know that  All mapping are relation, but the converse is not true .

Q: Let A = {1,2,3,4} and B = {A,B, C, D, E}. Consider the following relations and state whether…

A: A relation will be function if for each x∈A  there exists a unique b∈B with (a, b) ∈ f. In other…