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1 5 7 9 10 NOT 6 11 12 3 4 6 NOT 7 9 OR 11 6 10 AND 7 х OR NOT3AND Z 5 OR NOT 2 OR Y AND 1 AND 4 1 Y 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 C 0 1 0 0 0 0 0 0 C 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1*= x 0+X= X 1+X 1 Ox= 0 Idempotent Law XX %3D х X+X X xX = 0 X+X= 1 Inverse Law X+y y+x (X+y)+z = x+(y+z Commutative Law ху %3D ух (ху)z %3D x(уz) |X+yz = (x+y)(x+z) x(y+z) = xy+xz x(x+у) — х (xy) = X+7 Associative Law Distributive Law X+ху%3D х (X+y) = xy X = x Absorption Law DeMorgan's Law Double Complement Law

1 5 7 9 10 NOT 6 11 12 3 4 6 NOT 7 9 OR 11 6 10 AND 7 х OR NOT3AND Z 5 OR NOT 2 OR Y AND 1 AND 4 1 Y 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 C 0 1 0 0 0 0 0 0 C 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1*= x 0+X= X 1+X 1 Ox= 0 Idempotent Law XX %3D х X+X X xX = 0 X+X= 1 Inverse Law X+y y+x (X+y)+z = x+(y+z Commutative Law ху %3D ух (ху)z %3D x(уz) |X+yz = (x+y)(x+z) x(y+z) = xy+xz x(x+у) — х (xy) = X+7 Associative Law Distributive Law X+ху%3D х (X+y) = xy X = x Absorption Law DeMorgan's Law Double Complement Law

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Form boolean equations in POS and SOP forms from the truth table attached (PLEASE EXPLAIN ALL STEPS), then show steps to simplify using boolean identities (also attached). 


1 5 7 9 10 NOT 6 11 12 3 4 6 NOT 7 9 OR 11 6 10 AND 7 х OR NOT3AND Z 5 OR NOT 2 OR Y AND 1 AND 4 1 Y 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 C 0 1 0 0 0 0 0 0 C 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1
Transcribed Image Text:1 5 7 9 10 NOT 6 11 12 3 4 6 NOT 7 9 OR 11 6 10 AND 7 х OR NOT3AND Z 5 OR NOT 2 OR Y AND 1 AND 4 1 Y 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 C 0 1 0 0 0 0 0 0 C 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1
Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1*= x 0+X= X 1+X 1 Ox= 0 Idempotent Law XX %3D х X+X X xX = 0 X+X= 1 Inverse Law X+y y+x (X+y)+z = x+(y+z Commutative Law ху %3D ух (ху)z %3D x(уz) |X+yz = (x+y)(x+z) x(y+z) = xy+xz x(x+у) — х (xy) = X+7 Associative Law Distributive Law X+ху%3D х (X+y) = xy X = x Absorption Law DeMorgan's Law Double Complement Law
Transcribed Image Text:Boolean Identities Identity Name Identity Law Null (or Dominance) Law AND Form OR Form 1*= x 0+X= X 1+X 1 Ox= 0 Idempotent Law XX %3D х X+X X xX = 0 X+X= 1 Inverse Law X+y y+x (X+y)+z = x+(y+z Commutative Law ху %3D ух (ху)z %3D x(уz) |X+yz = (x+y)(x+z) x(y+z) = xy+xz x(x+у) — х (xy) = X+7 Associative Law Distributive Law X+ху%3D х (X+y) = xy X = x Absorption Law DeMorgan's Law Double Complement Law
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