HW2 - algebra. (10p) 6. Prove, that no Boolean algebra can...

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Homework #2 January 15, 2008 1 Homework #2 due January 28 at noon ECE 15a Winter 2008 For problems 1-6 supply the reasons for each step. (10p) 1. Write out the proof that a(a+b)=a in Theorem 4 (lecture #3), referring each step to the correct postulate. (10p) 2. Prove that in every Boolean algebra every triple of elements a, b,c satisfies the identity ab+bc+ca=(a+b)(b+c)(c+a). (10p) 3. Prove, that if a+x=b+x and a+x’=b+x’, then a=b. (hint: check the proof of Theo- rem 5 in lecture #3). (10p) 4. Prove, that if ax=bx and ax’=bx’, then a=b. (10p) 5. Show that the set {a,b,c,d} with operations (+) and (.) defined below is a Boolean
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Unformatted text preview: algebra. (10p) 6. Prove, that no Boolean algebra can have exactly three distinct elements. (10p) 7. Prove that if A and B are sets satisfying the relation A B, then A+BC=B(A+C) for every set C. This property is known as the modular law . 8. Do the following problems from CHR: (5p) (a) 2.16 (b) (5p) (b) 2.16 (d) (5p) (c) 2.17 (a) (5p) (d) 2.17 (c) + a b c d a a b c d b b b b b c c b c b d d b b d . a b c d a a a a a b a b c d c a c c a d a d a d ⊆...
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This note was uploaded on 01/13/2010 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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