HW2_Sol

HW2_Sol - ECE 15A Homework 2 Solutions 1. Write out the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 15A Homework 2 Solutions 1. Write out the proof that a(a+b) = a in theorem 4, referring each step to the correct postulate: a(a+b) = a aa + ab by Distributive Law a + ab by Theorem 2 a1+ab P2 a(1+b) by Distributive Law a=1a T2 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) ab+bc+ca b(a+c)+ca Distributive Law (b+ac)(a+c+ac) Distributive Law (b+a)(b+c)(a+a+c)(a+c+c) Distributive Law (b+a)(b+c)(a+c) 3. Prove, that if a + x = b + x and a + x’ = b + x’ , then a = b . a = a + ax + ax’ Thm 4 b = b + bx + bx’ Thm 4
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
a = a + ax + ax’ = aa + ax + ax’ + xx’ P2, P4 = a ( a + x) + x’( a + x) P3 = ( a + x ) ( a + x’) P3 = ( b + x ) ( b + x’) Given = bb + bx’ + xb + xx’ P3 = b + bx + bx’ P4 = b 4. Prove, that if ax = bx and ax’ = bx’ , then a = b . a = a ( x + x’) P4 = a x + a x P3 = b x + b x Given = b ( x + x ) P3 = b P 4 ==> a = b 5. Show that set {a,b,c,d} with operations (+) and (.) as defined is a Boolean algebra. To prove that the operations are a Boolean algebra, we have to show that the postulates P1- P4 (see lecture notes #3, slide 14) hold.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

HW2_Sol - ECE 15A Homework 2 Solutions 1. Write out the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online