{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CSE20 Lecture 9

CSE20 Lecture 9 - CSE 20 Lecture 9 Boolean Algebra CK Cheng...

This preview shows pages 1–9. Sign up to view the full content.

CSE 20 Lecture 9 Boolean Algebra CK Cheng Feb 11, 2010 Lecture notes 1

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

View Full Document
Theorems & Proofs P1: a+b = b+a, ab=ba P2: a+bc = (a+b)(a+c) a(b+c) = ab + ac P3: a + 0 = a, a1 = a P4: a + a’= 1, a a’= 0 2
Theorem 6: for every a in B, (a')' = a Proof: A is complement of a'. The complement of a‘ is unique Thus a = (a')' Theorem 7: (Absorption Law) For every pair a,b in B, a·(a+b) = a, a + a·b = a Proof: a(a+b) a+a·b = (a+0)(a+b) (P3) = a·1 + a·b (P3) = a+0·b (P2) = a(1+b) (P2) = a + 0 (P3) = a·1 (P3) = a (P3) = a (P3) 3

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

View Full Document
Theorem 8 For every pair a, b in B a + a’*b = a + b,a*(a’+ b) = a*b Proof: a + a’*b = (a + a’)(a + b) by P2 = (1)(a + b) by P4 = (a + b) by P3 a*(a’+ b) = a*a’+ a*b (by P3) = 0 + a*b (by P4) = a*b (by P3) 4
Theorem 9: De Morgan’s Law Theorem: For every pair a, b in set B: (a+b)’= a’b’, and (ab)’= a’+b’. Proof: We show that a+b and a’b’are complementary. According to P4, both of the following have to be true: (a+b) +a’b’= 1, (a+b)(a’b’) = 0 5

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

View Full Document
Theorem 9: De Morgan’s Law (cont.) statement justification (a+b)+a’b’ = 1 given (a+b+a’)(a+b+b’) = 1

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern