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Unformatted text preview: in some cases. (a) 3  (b) 0 ∈ N (c) For any real number x , ⌊ x ⌋ < ⌈ x ⌉ . (d) 3 is prime. (e) − 13  − 26 5. (3 points) State the contrapositive of the following statement, using logical equivalences to put it into a form where each “not” is on an individual (noncomplex) proposition. Show your work. If John is a muggle and Ellen is a Wizard, then the crystal is not blue. 6. (3 points) Complete the following de±nition, using precise mathematical English and/or notation. Your de±nition must not use the mod, remainder, or similar operators. If x and y are integers, x  y if and only if . . . 2...
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 Spring '08
 Erickson
 Logic, Natural number, noncomplex) proposition.

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