hw2_2011 - lecture#3(10p 4 Prove that if a and b are...

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Homework #2 due January 24 at noon ECE 15a Winter 2011 For problems 1-5 supply the reasons for each step. Please, use postulate and theorem numbers as in lecture notes #3. Similarly, the problem statements below follow the references to postulates and theorems according to lecture #3 notation. (10p) 1. Write out the proof that (a+b)’=a’b’ referring each step to the correct postulate P1-P4. You can also use Theorems 2-8. (10p) 2. Prove that in every Boolean algebra a(a+b)=a for every pair of elements a and b. In your proof, you can use only P1-P4 and Theorems 2-3. (10p) 3. Prove that if a+x=b+x and a+x’=b+x’, then a=b. (hint: check the proof of Theorem 5 in
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Unformatted text preview: lecture #3). (10p) 4. Prove that if a and b are elements of a Boolean algebra and ab’=0 then a+bc=b(a+c) for every element c in B. Use only P1-P4 in your proof. (15p) 5. Show that the set {a,b,c,d} with operations (+) and (.) defined below is a Boolean algebra. + a b c d . a b c d a a a a a a a b c d b a b b a b b b c c c a b c d c c c c c d a a d d d d c c d (15p) 6. Simplify the following expressions into a minimum sum of products: (a) 5p (((x+y)’+z)’w)’ (b) 5p (a+b)’cd’+a+b (c) 5p ((a+b)’+c’d)’ (15p) 7. Simplify each of the following expressions into a minimum product of sum form: (a) 5p ab+abc’+ac’d (b) 5p a+bc+def (c) 5p ab + bc = ac...
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