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Unformatted text preview: Sample First Midterm Key 1. a. A proposition is a sentence that is either true or false. b. Two propositional forms are equivalent iff they have the same truth table. c. This makes no sense. We know what a denial of a proposition is, and an open sentence is not a proposition. [Note: I might ask this kind of question in order to be sure people do not simply try to &quot;wing it&quot; on the definitions  be sure I am asking you to define one of our actual concepts.] 2. We know that P =&gt; (Q or R) is equivalent to ~P or (Q or R). This is equivalent to (~P or R) or Q, which is in turn equivalent to ~(~P or R) =&gt; Q, which is equivalent to (P and ~R) =&gt; Q. [I have used the general equivalence P =&gt; Q &lt;=&gt; ~P or Q in both directions here.] 3. a. English: There is some positive number e such that f is bounded above by L + e and bounded below by L  e for all x except possibly x = a. Negation: (all e) {e &gt; 0 =&gt; (exists d)[d&gt;0 and (exists x) (0 &lt; xa &lt; d and f(x)  L geq e)]} English: No matter what positive e we consider, there is some d...
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This note was uploaded on 03/18/2012 for the course MAT 108 taught by Professor Staff during the Winter '10 term at UC Davis.
 Winter '10
 Staff

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