Hmwk1_rev - Homework#1 due January 22 at noon ECE 15a...

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Homework #1 January 17, 2007 1 Homework #1 due January 22 at noon ECE 15a Winter 2007 1. Expand the following into a polynomial having as few terms as possible: (2p) (a) (x+y’x)(x+yz) (3p) (b) (x+y)(x’+y)(x+y’)(x’+y’) 2. Factor the following into linear factors: (1p) (a) xy+zw (2p) (b) x+y(z+w) (2p) (c) abc+a’d 3. Using Venn diagrams, show that if A and B are sets, then (5p)(a) (A+B)’ = A’B’ (5p) (b) X(Y+Z) = XY + XZ 4. Simplify the following: (5p) (a) (a+b’+c)’(ab+a’c’) (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’y’z’) (10p) 5. Write out the proof of Theorems 1 and 2 (See lecture #2), based on the fact that
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