1)Let S be the set of all students at a college. Define a relation on the...

1)Let S be the set of all students at a college. Define a relation on the set S by the rule that two people are related if they live less than 2 miles apart. Is this relation an equivalence relation on S? Justify your answer.

2) Define another relation on the set S from problem 5 by defining two people as related if they have the same classification (freshman, sophomore, junior, senior or graduate student). Is this an equivalence relation on S? Justify.

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Colby Messinger answered 2 years ago

1)Let S be the set of all students at a college. Define a relation on the...

1)Let S be the set of all students at a college. Define a relation on the set S by the rule that two people are related if they live less than 2 miles apart. Is this relation an equivalence relation on S? Justify your answer. 2) Define another relation on the set S from problem 5 by defining two people as related if they have the same classification (freshman, sophomore, junior, senior or graduate student). Is this an equivalence relation...

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by...

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Let S = {-3, -2, -1, 0, 1, 2, 3}. Define a relation R on S...

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Let A = R x R, and let a relation S be defined as: “(x1, y1)...

Let A = R x R, and let a relation S be defined as: “(x1, y1) S (x2, y2) ⬄ points (x1, y1) and (x2, y2)are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you must give a counterexample.

Given a natural number q ≥ 1, define a relation ∼ on the set Z by...

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1)Let S be the set of all students at a college. Define a relation on the...

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