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hmwk2 - algebra(10p 6 Prove that no Boolean algebra can...

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Homework #2 January 15, 2007 1 Homework #2 due January 29 at noon ECE 15a Winter 2007 For problems 1-7 supply the reasons for each step. (10p) 1. Write out the proof that a0=0 in Theorem 3 (lecture #3), referring each step to the correct postulate. (10p) 2. Prove that in every Boolean algebra a+a’b=a+b for every pair of elements a and b. (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 elements of a Boolean algebra B satisfying the relation a b, then a+bc=b(a+c) for every element c in B. 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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