Homework #1January 17, 20071Homework #1due January 22 at noonECE 15a Winter 20071. 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’d3. Using Venn diagrams, show that if A and B are sets, then (5p)(a) (A+B)’ = A’B’(5p) (b) X(Y+Z) = XY + XZ4. 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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following conditions, Merchant, certain sets A,B,C,D