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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
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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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')
Transcribed Image Text: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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