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Unformatted text preview: . Name; K E’ g MATH 108 ‘ Section 1
First Midterm October 22, 2010 Answer all questions on these pages. If you need more space, write on the back of the previous
page and indicate that you have done so. Since this course emphasizes the basics and rigor, your  justiﬁcation of an answer is more important than the answer  so always give a clear and complete
justiﬁcation unless you are instructed not to do so. 1. In each part below, give the deﬁnition:
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a. The conjunction of propositions P and Q. t, i
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’v‘fﬂxaﬂg m“ AomAlgch 2. Indicate if each of the following statements is true or false. If a statement is true, prove it directly (do not cite any theorems). If it is false, give a counter example:
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3. a. Negate the following expression: (3x)(Vy)(P(x,y) A R(x) => (Elz)(Q(z) v S(z))) <12) ( m (3 p (POW) /\ mm (V2) (~a (am/9)) (Problem 3 continues on next page) b. In the universe of Q, give proofs of the following theorems: _ i (VY) (3X) (X  y > 0)
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gc/“Cur ck CJ<VQM X Ive—F \/ ': TM“ >97: X*C>L—H)'; vL’X*l‘=~'\ so, 4. a. State the tautology that justiﬁes
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(Pt; Q) < :2) [ (l’ch'Q) :>({z A442?) b. Prove that if x2 is not divisible by 4 then x is odd. U 2 Z Use vatm fog1410 n .
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5. a. Let A = {a, {a}, E, {b}}. How many elements are in the power set ‘P(A): ; ‘36
In each case below, circle any of the three symbols in the brackets that applies: (2°) i. z @gQA. ii. a @c,g] A.
iii. {z} [e,©@ A.
iv. 6 ’.P(A). (Problem 5 continues on next page) b. HA and B are sets,prove that AQB =9 CP(A) Q ’P(B).
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7. Prove that WOP => PMI. ’ (12) arrow SCAN MA awes‘
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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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