06: Logical Disjunctions

Boolean Disjunctions

Introduction

A Boolean disjunction is a conditional statement where you combine more than one condition but you are trying to know whether at least one of the conditions is false. This operation is commonly represented by a Boolean operator named -or. The primary formula to use it is:

condition1 -or condition2

Each condition is formulated as a Boolean operation:

operand1 Boolean-operator operand2 -or operand3 Boolean-operator operand4

As seen with conjunctions, the whole disjunction operation can be assigned to a Boolean variable or it can be written in the parentheses of a conditional statement.

This operation is referred to as a logical disjunction, or a Boolean disjunction, or simply a disjunction. This operation is resumed as follows:

The first condition, condition1, is checked. If that first condition is true, the second condition is not checked and the whole operation produces a true result
The first condition, condition1, is checked. If that first condition is false, then the second condition, condition2, is checked. If that second condition is true, then the whole operation produces a true result
In the same way, if both conditions are true, the whole operation produces a true result
If both conditions are false, the whole operation produce a false result

A Boolean Operator for a Disjunction

When you are performing a logical disjunction, you can use any of the comparison operators we saw already (!, -eq, -ne, -lt, -le, -gt, -ge, and -not). When we studied conjunctions, we saw that you cannot logically use the same variable in two equality or non-equality conditions of a conjunction. In a disjunction, you can use the same variable or different variables in conditions. Here are examples that perform logical exclusions:

Write-Host '========================================================================================================='
Write-Host 'Job Requirements Evaluation'
Write-Host '---------------------------------------------------------------------------------------------------------'
# Do you hold a degree - Undergraduate or Graduate (y/n)?
$degree = 'y'
# Are you a certified programmer (Microsoft, Oracle, etc) (Type True or False)?
$certified = $true

if( $degree -eq 'y' -or $certified -eq $true ) {
    Write-Host "Candidate holds a degree: $degree"
    Write-Host "Candidate is certified:   $certified"
    Write-Host '---------------------------------------------------------------------------------------------------------'
    Write-Host 'Congratulations: We need to schedule the next interview (Human Resources) for you.'
}
else {
    Write-Host 'This job requires either a college degree or a professional certification in application programming.'
}

Write-Host '========================================================================================================='

This would produce:

PS C:\Windows\System32> C:\Exercises\Disjunctions.ps1
=========================================================================================================
Job Requirements Evaluation
---------------------------------------------------------------------------------------------------------
Candidate holds a degree: y
Candidate is certified:   True
---------------------------------------------------------------------------------------------------------
Congratulations: We need to schedule the next interview (Human Resources) for you.
=========================================================================================================

As seen with conjunctions, to make your code easy to read, you can include each condition in its own parentheses. Here are examples:

$name       = 'Gabrielle Towa'
$timeWorked = 42.50
$status     = 'Part-Time'
# The first condition is True while the second condition is False:
$verdict = ($status -eq 'Part-Time') -or ($status -eq 'Intern')

Write-Host 'Employee Name:              ' $name
Write-Host 'Time Worked:                ' $timeWorked
Write-Host 'Employment Status:          ' $status
Write-Host 'Condition-1 OR Condition-2: ' $verdict
Write-Host '----------------------------------------------------------'

if($verdict -eq $true) {
    Write-Host 'The time sheet has been approved.'
}
else {
    Write-Host 'Part-time employees are not allowed to work overtime.'
}

Write-Host '=========================================================='

$name       = 'Stephen Anders'
$status     = 'Seasonal'
$timeWorked = 38.00
# The first condition is False while the second condition is True:
$verdict    = ($status -eq 'Full-Time') -or ($status -eq 'Seasonal')

Write-Host 'Employee Name:              ' $name
Write-Host 'Time Worked:                ' $timeWorked
Write-Host 'Employment Status:          ' $status
Write-Host 'Condition-1 OR Condition-2: ' $verdict
Write-Host '----------------------------------------------------------'

if($verdict -eq $true) {
    Write-Host 'The time sheet has been approved.'
}
else {
    Write-Host 'Time Sheet under review.'
}

Write-Host '=========================================================='

$name       = 'Rose Sandt'
$status     = 'Full-Time'
$timeWorked = 44.00
# Both conditions are True:
$verdict    = ($status -eq 'Full-Time') -or ($status -eq 'Seasonal')

Write-Host 'Employee Name:              ' $name
Write-Host 'Time Worked:                ' $timeWorked
Write-Host 'Employment Status:          ' $status
Write-Host 'Condition-1 OR Condition-2: ' $verdict
Write-Host '----------------------------------------------------------'

if($verdict -eq $true) {
    Write-Host 'The time sheet has been approved.'
}
else {
    Write-Host 'Part-time and seasonal employees must consult the management.'
}

Write-Host '=========================================================='

$name       = 'Joseph Lee'
$status     = 'Intern'
$timeWorked = 36.50
# Both conditions are False:
$verdict    = ($status -eq 'Unknown') -or ($status -eq 'No Availability')

Write-Output 'Employee Name:              ' $name
Write-Output 'Time Worked:                ' $timeWorked
Write-Output 'Employment Status:          ' $status
Write-Output 'Condition-1 OR Condition-2: ' $verdict
Write-Output '----------------------------------------------------------'

if($verdict -eq $true) {
    Write-Host 'Employees time sheets are subject to approval.'
}
else {
    Write-Host 'New employees must consult the Human Resources department.'
}

Write-Host '=========================================================='

This would produce:

PS C:\Windows\System32> C:\Exercises\Disjunctions.ps1
Employee Name:               Gabrielle Towa
Time Worked:                 42.5
Employment Status:           Part-Time
Condition-1 OR Condition-2:  True
----------------------------------------------------------
The time sheet has been approved.
==========================================================
Employee Name:               Stephen Anders
Time Worked:                 38
Employment Status:           Seasonal
Condition-1 OR Condition-2:  True
----------------------------------------------------------
The time sheet has been approved.
==========================================================
Employee Name:               Rose Sandt
Time Worked:                 44
Employment Status:           Full-Time
Condition-1 OR Condition-2:  True
----------------------------------------------------------
The time sheet has been approved.
==========================================================
Employee Name:               Joseph Lee
Time Worked:                 36.5
Employment Status:           Intern
Condition-1 OR Condition-2:  False
----------------------------------------------------------
New employees must consult the Human Resources department.
==========================================================

Disjunction Equality

Remember that, in a Boolean conjunction or disjunction, you use two conditions and each condition performs its own comparison. As we saw with conjunctions, each condition of a disjunction can use its own variable for its comparison. Here is an example we saw in our introduction:

Write-Host '========================================================================================================='
Write-Host 'Job Requirements Evaluation'
Write-Host '---------------------------------------------------------------------------------------------------------'
# Do you hold a degree - Undergraduate or Graduate (y/n)?
$degree = 'y'
# Are you a certified programmer (Microsoft, Oracle, etc) (Type True or False)?
$certified = $true

if( ($degree -eq 'y') -or ($certified -eq $true) ) {
    Write-Output "Candidate holds a degree: $degree"
    Write-Output "Candidate is certified:   $certified"
    Write-Host '---------------------------------------------------------------------------------------------------------'
    Write-Host 'Congratulations: We need to schedule the next interview (Human Resources) for you.'
}
else {
    Write-Host 'This job requires either a college degree or a professional certification in application programming.'
}

Write-Host '========================================================================================================='

Combining Disjunctions

You can create a conditional statement that includes as many disjunctions as you want. The formula to follow is:

condition1 -or condition2 -or . . . -or condition_n

The rule is: If any one of the individual operations is true, the whole operation is true. The whole operation is false only if all the operations are false. Here is an example that uses three conoditions:

Write-Host '================================================================'
Write-Host 'Levels of Security Clearance:'
Write-Output '0. Unknown or None'
Write-Output '1. Non-Sensitive'
Write-Output '2. National Security - Non-Critical Sensitive'
Write-Output '3. National Security - Critical Sensitive'
Write-Output '4. National Security - Special Sensitive'

$level = 3
Write-Host '================================================================'
        
if( $level -eq 2 -or $level -eq 3 -or $level -eq 4 ) {
    Write-Host "Leve of Security Clearance: $level"
    Write-Host 'Company Decision:           Welcome on board.'
}
else {
    Write-Host 'We will get back to you...'
}

Write-Host '================================================================'

This would produce:

PS C:\Windows\System32> C:\Exercises\Disjunctions.ps1
================================================================
Levels of Security Clearance:
0. Unknown or None
1. Non-Sensitive
2. National Security - Non-Critical Sensitive
3. National Security - Critical Sensitive
4. National Security - Special Sensitive
================================================================
Leve of Security Clearance: 3
Company Decision:           Welcome on board.
================================================================

Once again, remember that, to make your code easier to read, you can include each condition in its own parentheses. Here are examples:

Write-Host '=========================================='
Write-Host ' - Amazing DeltaX - State Income Tax -'
Write-Host '=========================================='

Write-Host 'States'
Write-Output ' AK - Alaska'
Write-Output ' AR - Arkansas'
Write-Output ' CO - Colorado'
Write-Output ' FL - Florida'
Write-Output ' GA - Georgia'
Write-Output ' IL - Illinois'
Write-Output ' IN - Indiana'
Write-Output ' KY - Kentucky'
Write-Output ' MA - Massachusetts'
Write-Output ' MI - Michigan'
Write-Output ' MO - Missouri'
Write-Output ' MS - Mississippi'
Write-Output ' NV - Nevada'
Write-Output ' NH - New Hampshire'
Write-Output ' NC - North Carolina'
Write-Output ' PA - Pennsylvania'
Write-Output ' SD - South Dakota'
Write-Output ' TN - Tennessee'
Write-Output ' TX - Texas'
Write-Output ' UT - Utah'
Write-Output ' WA - Washington'
Write-Output ' WY - Wyoming'

$abbr    = "MA"
$taxRate = 0.00
        
if( ($abbr -eq "IL") -or ($abbr -eq "UT") ) {
    $taxRate = 4.95
}
elseif( ($abbr -eq "KY") -or ($abbr -eq "MA") -or ($abbr -eq "NH") ) {
    $taxRate = 5.00
}
elseif( ($abbr -eq "FL") -or
        ($abbr -eq "NV") -or
        ($abbr -eq "TX") -or
        ($abbr -eq "WA") -or
        ($abbr -eq "WY") ) {
    $taxRate = 0.00
}

$grossSalary = 2458.95

$taxAmount = $grossSalary * $taxRate / 100.00
$netPay    = $grossSalary - $taxAmount

Write-Host '============================================'
Write-Host ' - Amazing DeltaX - State Income Tax -'
Write-Host '--------------------------------------------'
Write-Host "Gross Salary: $grossSalary"
Write-Host "Tax Rate:     $taxRate"
Write-Host '--------------------------------------------'
Write-Host "Tax Amount:   $taxAmount"
Write-Host "Net Pay:      $netPay"
Write-Host '============================================'

This would produce:

PS C:\Windows\System32> C:\Exercises\Disjunctions.ps1
==========================================
 - Amazing DeltaX - State Income Tax -
==========================================
States
 AK - Alaska
 AR - Arkansas
 CO - Colorado
 FL - Florida
 GA - Georgia
 IL - Illinois
 IN - Indiana
 KY - Kentucky
 MA - Massachusetts
 MI - Michigan
 MO - Missouri
 MS - Mississippi
 NV - Nevada
 NH - New Hampshire
 NC - North Carolina
 PA - Pennsylvania
 SD - South Dakota
 TN - Tennessee
 TX - Texas
 UT - Utah
 WA - Washington
 WY - Wyoming
============================================
 - Amazing DeltaX - State Income Tax -
--------------------------------------------
Gross Salary: 2458.95
Tax Rate:     5
--------------------------------------------
Tax Amount:   122.9475
Net Pay:      2336.0025
============================================

Combining Conjunctions and Disjunctions

You can create a logical expression that combines conjunctions and disjunctions. Here is an example:

Write-Host 'Electric Bill Evaluation'
Write-Host '======================================================'
$zipCode          = 20620
$counterStart     = 10089
$counterEnd       = 11126
$days             = 29

$custChargeRate   = 0.49315
$nrgChargeRate    = 0.16580
$envChargeRate    = 0.00043

$electricUse      = $counterEnd - $counterStart

$custCharge       = $days        * $custChargeRate
$energyCharge     = $electricUse * $nrgChargeRate
$envControlCharge = $electricUse * $envChargeRate

$serviceTotal     = 0

# Let's imagine a fictitious scenario where the government 
# wants to assist people in a certain group of ZIP codes by 
# giving them a small discount ($3.15) in their electric bill.
if( ($zipCode -ge 20628 -and $zipCode -le 20685 ) -or
    ($zipCode -ge 21110 -and $zipCode -le 21120 ) -or
    ($zipCode -ge 21735 -and $zipCode -le 21795 ) ) {
    $serviceTotal = $custCharge + $energyCharge + $envControlCharge - 3.15
}
else {
    $serviceTotal = $custCharge + $energyCharge + $envControlCharge
}

Write-Output 'Electric Bill Summary:'
Write-Output '======================================================'
Write-Output "Counter Reading Start:         $counterStart"
Write-Output "Counter Reading End:           $counterEnd"
Write-Output "Total Electric Use:            $electricUse"
Write-Output "Number of Days:                $days"
Write-Output "Customer ZIP-Code:             $zipCode"
Write-Output '======================================================'
Write-Output 'Energy Charge Credit'
Write-Output '======================================================'
Write-Output "Customer Charge Rate:          $custChargeRate"
Write-Output "Customer Charge:               $custCharge"
Write-Output '------------------------------------------------------'
Write-Output "Energy Charge Rate:            $nrgChargeRate"
Write-Output "Energy Charge:                 $energyCharge"
Write-Output '------------------------------------------------------'
Write-Output "Energy Charge Rate:            $envChargeRate"
Write-Output "Environmental Control Charge:  $envControlCharge"
Write-Output '------------------------------------------------------'
Write-Output "Electric Servive Total:        $serviceTotal"
Write-Output '======================================================'

This would produce:

PS C:\Windows\System32> C:\Exercises\Disjunctions.ps1
Electric Bill Evaluation
======================================================
Electric Bill Summary:
======================================================
Counter Reading Start:         10089
Counter Reading End:           11126
Total Electric Use:            1037
Number of Days:                29
Customer ZIP-Code:             20620
======================================================
Energy Charge Credit
======================================================
Customer Charge Rate:          0.49315
Customer Charge:               14.30135
------------------------------------------------------
Energy Charge Rate:            0.1658
Energy Charge:                 171.9346
------------------------------------------------------
Energy Charge Rate:            0.00043
Environmental Control Charge:  0.44591
------------------------------------------------------
Electric Servive Total:        186.68186
======================================================

Once again, to make your code easy to read, you can include each condition or group in its own parentheses. Here are examples:

Write-Host 'Electric Bill Evaluation'
Write-Host '======================================================'
$zipCode          = 20620
$counterStart     = 10089
$counterEnd       = 11126
$days             = 29

$custChargeRate   = 0.49315
$nrgChargeRate    = 0.16580
$envChargeRate    = 0.00043

$electricUse      = $counterEnd - $counterStart

$custCharge       = $days        * $custChargeRate
$energyCharge     = $electricUse * $nrgChargeRate
$envControlCharge = $electricUse * $envChargeRate

$serviceTotal     = 0

# Let's imagine a fictitious scenario where the government 
# wants to assist people in a certain group of ZIP codes by 
# giving them a small discount ($3.15) in their electric bill.
if( ( ($zipCode -ge 20628) -and ($zipCode -le 20685) ) -or
    ( ($zipCode -ge 21110) -and ($zipCode -le 21120) ) -or
    ( ($zipCode -ge 21735) -and ($zipCode -le 21795) ) ) {
    $serviceTotal = $custCharge + $energyCharge + $envControlCharge - 3.15
}
else {
    $serviceTotal = $custCharge + $energyCharge + $envControlCharge
}

Write-Host 'Electric Bill Summary:'
Write-Host '======================================================'
Write-Output "Counter Reading Start:         $counterStart"
Write-Output "Counter Reading End:           $counterEnd"
Write-Output "Total Electric Use:            $electricUse"
Write-Output "Number of Days:                $days"
Write-Output "Customer ZIP-Code:             $zipCode"
Write-Host '======================================================'
Write-Host 'Energy Charge Credit'
Write-Host '======================================================'
Write-Output "Customer Charge Rate:          $custChargeRate"
Write-Output "Customer Charge:               $custCharge"
Write-Host '------------------------------------------------------'
Write-Host "Energy Charge Rate:            $nrgChargeRate"
Write-Host "Energy Charge:                 $energyCharge"
Write-Host '------------------------------------------------------'
Write-Output "Energy Charge Rate:            $envChargeRate"
Write-Output "Environmental Control Charge:  $envControlCharge"
Write-Host '------------------------------------------------------'
Write-Output "Electric Servive Total:        $serviceTotal"
Write-Host '======================================================'


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