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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 (non-complex) 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
- Logic, Natural number, non-complex) proposition.