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Boolean Operators
Defined by truth tables and applied in search expressions
Building a Truth Tablep q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
Building a Truth Tablep q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
The number of rows in a truth table is 2n, where n is the
number of terms in the table.
Building a Truth TableNegation
p q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
The truth-value of ~p is always the opposite of p. This is essentially what contradiction looks like.
Building a Truth Table Boolean AND
p q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
The expression p • q (p AND q) evaluates to TRUE only when both p and q are TRUE.
Building a Truth TableBoolean OR
p q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
The expression p v q ( p OR q; inclusive OR) evaluates to TRUE when either p or q is TRUE.
Building a Truth TableAll Relations
p q ~p p • q p v q
T T F T T
T F F F T
F T T F T
F F T F F
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.
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
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
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
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
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
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
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
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
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
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
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
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