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HW1 - Homework#1 due January 23 at noon ECE 15a Winter 2008...

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Homework #1 January 8, 2008 1 Homework #1 due January 23 at noon ECE 15a Winter 2008 1. Expand the following into a polynomial having as few terms as possible: (2p) (a) (ab’+bc)(a’b’+ac+bc) (3p) (b) (x+y)(x’+y)(x+y’)(x’+y’) 2. Factor the following into linear factors: (1p) (a) x’y+zw’ (2p) (b) ax’+ay(x+z) (2p) (c) a’bc+ad 3. Using Venn diagrams, show that if A and B are sets, then (5p)(a) (A’+B)’ = AB’ (5p) (b) X(Y+Z) = XY + XZ 4. Simplify the following: (5p) (a) (a’+b’+c)(a’b+ac’)’ (5p) (b) (x’y+xy+x’y)(x’y+zw) (5p) (c) abx’+abx+x’abx (5p) (d) (xy’+xy+x’y’)(x+y’+z+x’yz’) (10p) 5. Write out the proof of Theorems 1 and 2 (See lecture #2), based on the fact that
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