Boolean Operators

1
Boolean Operators

• Defined by truth tables and applied in search
  expressions

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Building a Truth Table
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Building a Truth Table
The number of rows in a truth table is 2n, where
n is the number of terms in the table.
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Building a Truth TableNegation
The truth-value of p is always the opposite of
p. This is essentially what contradiction looks
like.
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Building a Truth Table Boolean AND
The expression "p q" evaluates to TRUE only
when both p and q are TRUE.
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Building a Truth TableBoolean OR
The expression p v q ( also written "p OR q"
inclusive OR) evaluates to TRUE when either p or
q is TRUE.
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Building a Truth TableAll Relations
The three operators illustrated here are the
basis of most database searches.
8
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
9
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
10
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
11
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
12
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
13
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
14
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
15
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
16
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
17
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
18
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
19
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3
20
In the music store...
C - CD e - electronica 1 - single disk pkg. D -
DVD h - hip hop 2 - double disk pkg. S - Super
Audio CD m - metal 3 - triple disk pkg.
All CDs C Everything that is not a Super
Audio CD S All electronica DVDs D e DVDs
that are not metal D (m) All CDs and
DVDs C v D Hip hop CDs except triple disk
pkgs. (h C) 3