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Boolean Operators Defined by truth tables and applied in search expressions Building a Truth Table Building a Truth Table The number of rows in a truth table is 2 n , where n is the number of terms in the table. Building a Truth Table Negation

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boolean operators

Boolean Operators

Defined by truth tables and applied in search expressions

building a truth table3
Building a Truth Table

The number of rows in a truth table is 2n, where n is the number of terms in the table.

building a truth table negation
Building a Truth TableNegation

The truth-value of ~p is always the opposite of p. This is essentially what contradiction looks like.

building a truth table boolean and
Building a Truth TableBoolean AND

The expression "p & q" evaluates to TRUE only when both p and q are TRUE.

building a truth table boolean or
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.

building a truth table all relations
Building a Truth TableAll Relations

The three operators illustrated here are the basis of most database searches.

slide8
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - triple disk pkg.

slide9
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide10
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide11
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide12
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide13
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide14
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide15
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide16
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide17
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide18
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide19
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

slide20
In the music store...

C - CD e - electronica1 - single disk pkg.

D - DVD h - hip hop2 - double disk pkg.

S - Super Audio CD m - metal3 - 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

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