2.1Demonstrate the validity of the following identities by means of truth tables:(a) DeMorgan's theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x' + y' + z'(b) The distributive law: x + yz (x + y)(x + z)(c) The distributive law: x(y + z) = xy + xz(d) The associative law: x + (y + z) = (x + y) + z(e) The associative law and x(yz) = (xy)z2.2Simplify the following Boolean expressions to a minimum number of literals:(a)* xy + xy'(c)* xyz + x'y + xyz'(e) xyz' + x'yz + xyz + x'yz'(b)* (x + y)(x + y')(d)* (A + B)'(A' + B')'(f) (x + y + z')(x' +y' + z)2.3Simplify the following Boolean expressions to a minimum number of literals:(а)* АВС + A'В + АВС"(c)* (x + y)'(x' + y')(e)* (BC' + A'D)(AB' + CD')(b)" x'yz + xz(d) xy + x(wz + wz')(f) (x + y' + z')(x'+ z')

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Demonstrate the validity of the following identities by means of truth tables: (a) DeMorgan's theorem for three variables: (x +y+ z)' x'y'z' and (xyz)' x' + y' +z' (b) The distributive law: x + yz (x+ y)(x + z) (c) The distributive law: x(y + z) = xy + xz %3D

Demonstrate the validity of the following identities by means of truth tables: (a) DeMorgan's theorem for three variables: (x +y+ z)' x'y'z' and (xyz)' x' + y' +z' (b) The distributive law: x + yz (x+ y)(x + z) (c) The distributive law: x(y + z) = xy + xz %3D

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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Question

2.1
Demonstrate the validity of the following identities by means of truth tables:
(a) DeMorgan's theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x' + y' + z'
(b) The distributive law: x + yz (x + y)(x + z)
(c) The distributive law: x(y + z) = xy + xz
(d) The associative law: x + (y + z) = (x + y) + z
(e) The associative law and x(yz) = (xy)z
2.2
Simplify the following Boolean expressions to a minimum number of literals:
(a)* xy + xy'
(c)* xyz + x'y + xyz'
(e) xyz' + x'yz + xyz + x'yz'
(b)* (x + y)(x + y')
(d)* (A + B)'(A' + B')'
(f) (x + y + z')(x' +y' + z)
2.3
Simplify the following Boolean expressions to a minimum number of literals:
(а)* АВС + A'В + АВС"
(c)* (x + y)'(x' + y')
(e)* (BC' + A'D)(AB' + CD')
(b)" x'yz + xz
(d) xy + x(wz + wz')
(f) (x + y' + z')(x'+ z')

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