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
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
Related questions
Question
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).
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
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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