HW1-Sol

# HW1-Sol - ECE 15A Homework Solution 1 1 Expand the...

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ECE 15A – Homework Solution # 1 1. Expand the following into a polynomial having as few terms as possible: a. (x+y’x)(x+yz) =(x+y’)(x+x)(x+yz) from using law 3b =x(x+y’)(x+yz) where x+x=x from law 4b, =x(x+yz) where x(x+y’)=x from law 5a, =x(x+yz) again by using law 5a. =x b. (x+y)(x’+y)(x+y’)(x’+y’) =(y+xx’)(y’+xx’) by using law 3b =yy’ where xx’=0 by law 6a =0 where yy’=0 by law 6a 2. Factor the following into linear factors: a. xy+zw (x+zw)(y+zw) using law 3b (x+z)(x+w)(y+z)(y+w) using law 3b Factors x+z, x+w, y+z, and y+w are linear factors b. x+y(z+w) (x+y)(x+z+w) using law 3b Factors x+y, and x+z+w are linear factors c. abc+a’d (a+a’d)(bc+a’d) using law 3b (a+a’)(a+d)(b+a’d)(c+a’d) using law 3b (a+d)(b+a’)(b+d)(c+a’)(c+d) using law 3b, where a+a’=1 by law 6b Factors a+d, b+a’, b+d, c+a’ and c+d are linear factors 3. Using Venn diagrams, show that if A and B are sets, then 1

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a. B A A+B B A (A+B)' B A A' B A A'B' A B' B b.
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HW1-Sol - ECE 15A Homework Solution 1 1 Expand the...

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