Suppose ? is a binary relation that can be applied to any two natural numbers (i.e....
Suppose ? is a binary relation that can be applied to any two natural numbers (i.e. positive integers). Given any two ?, ? ∈ ℕ, we say ??? if ? is wholly divisible by ? (i.e. without any remainder). For example, 8 ? 2 because 8 2 = 4, but 7 ¬? 3 because 7 3 = 2 1 3 . Hint: For any question below to which the answer is “no,” a single counterexample is all that is required as proof.
a. Is ? reflexive? Explain your answer.
b. Is ? complete? Explain your answer.
c. Is ? transitive? Explain your answer.
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Suppose ? is a binary relation that can be applied to any two
natural numbers (i.e....
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Can you #2 and #3?
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Can you #2 and #3?
6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determine if it is an equivalence relation on A. If it is, describe the equivalence classes. If it is not determine which properties of an equivalence relation fail. (a) a Hb a and b are the same age in (in years). (b) a Gb a and b have grandparent in common. 2) Consider the relation S(x,y):x...
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