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Logical Conjunction and Disjunction

 

Logical Conjunction

 

Introduction

As mentioned already, you can nest one conditional statement inside of another. To illustrate, imagine you create a workbook that would be used by a real estate company that sells houses. You may face a customer who wants to purchase a single family house but the house should not cost more than $550,001. To implement this scenario, you can first write a procedure that asks the user to specify a type of house and then a conditional statement would check it. Here is an example:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Value As Double
        
    TypeOfHouse = "Unknown"

    Choice = CInt(InputBox("Enter the type of house you want to purchase" _
		  & vbCrLf & _
                  "1. Single Family" & vbCrLf & _
                  "2. Townhouse" & vbCrLf & _
                  "3. Condominium" & vbCrLf & vbCrLf & _
                  "You Choice? "))
    Value = CDbl(InputBox("Up to how much can you afford?"))

    TypeOfHouse = Choose(Choice, "Single Family", _
                                 "Townhouse", _
                                 "Condominium")
End Sub

If the user selects a single family, you can then write code inside the conditional statement of the single family. Here is an example:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Value As Double
        
    TypeOfHouse = "Unknown"

    Choice = CInt(InputBox("Enter the type of house you want to purchase" _
		  & vbCrLf & _
                  "1. Single Family" & vbCrLf & _
                  "2. Townhouse" & vbCrLf & _
                  "3. Condominium" & vbCrLf & vbCrLf & _
                  "You Choice? "))
    Value = CDbl(InputBox("Up to how much can you afford?"))

    TypeOfHouse = Choose(Choice, "Single Family", _
                                 "Townhouse", _
                                 "Condominium")

    If Choice = 1 Then
        MsgBox("Desired House Type:      " & vbTab & TypeOfHouse & vbCrLf & _
               "Maximum value afforded:  " & vbTab & FormatCurrency(Value))
    End If
End Sub

Here is an example of running the program:

Logical Conjunction

Logical Conjunction

Logical Conjunction

In that section, you can then write code that would request and check the value the user entered. If that value is valid, you can take necessary action. Here is an example:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Value As Double
        
    TypeOfHouse = "Unknown"

    Choice = CInt(InputBox("Enter the type of house you want to purchase" _
          & vbCrLf & _
                  "1. Single Family" & vbCrLf & _
                  "2. Townhouse" & vbCrLf & _
                  "3. Condominium" & vbCrLf & vbCrLf & _
                  "You Choice? "))
    Value = CDbl(InputBox("Up to how much can you afford?"))

    TypeOfHouse = Choose(Choice, "Single Family", _
                                 "Townhouse", _
                                 "Condominium")
                                 
    If Choice = 1 Then
        MsgBox ("Desired House Type:      " & vbTab & TypeOfHouse & vbCrLf & _
                "Maximum value afforded:  " & vbTab & FormatCurrency(Value))
            
        If Value <= 550000 Then
            MsgBox ("Desired House Matched")
        Else
            MsgBox ("The House Doesn't Match the Desired Criteria")
        End If
    End If
End Sub

A Conditional Conjunction

Using conditional nesting, we have seen how you can write one conditional statement that depends on another. But you must write one first condition, check it, then nest the other condition. This works fine and there is nothing against it.

To provide you with an alternative, you can use what is referred to as a logical conjunction. It consists of writing one If...Then expression that checks two conditions at the same time. To illustrate, once again consider a customer who wants to purchase a single family home that is less than $550,000. You can consider two statements as follows:

  1. The house is single family
  2. The house costs less than $550,000

To implement it, you would need to write an If...Then condition as:

If The house is single family AND The house costs less than $550,000 Then

    Validate

End If

In the Visual Basic language, the operator used to perform a logical conjunction is And. Here is an example of using it:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Value As Double

    TypeOfHouse = "Unknown"

    Choice = _
	  CInt(InputBox("Enter the type of house you want to purchase" & vbCrLf & _
                        "1. Single Family" & vbCrLf & _
                        "2. Townhouse" & vbCrLf & _
                        "3. Condominium" & vbCrLf & vbCrLf & _
                        "You Choice? "))
    Value = CDbl(InputBox("Up to how much can you afford?"))

    TypeOfHouse = Choose(Choice, "Single Family", _
                                 "Townhouse", _
                                 "Condominium")

    If TypeOfHouse = "Single Family" And Value <= 550000 Then
        MsgBox("Desired House Type:      " & vbTab & TypeOfHouse & vbCrLf & _
               "Maximum value afforded:  " & vbTab & FormatCurrency(Value))
        MsgBox("Desired House Matched")
    Else
        MsgBox("The House Doesn't Match the Desired Criteria")
    End If
End Sub

Here is an example of running the program:

Logical Conjunction

Logical Conjunction

Logical Conjunction

By definition, a logical conjunction combines two conditions. To make the program easier to read, each side of the conditions can be included in parentheses. Here is an example:

Sub Exercise
    . . . No Change

    If (TypeOfHouse = "Single Family") And (Value <= 550000) Then
        MsgBox("Desired House Type:      " & vbTab & TypeOfHouse & vbCrLf & _
               "Maximum value afforded:  " & vbTab & FormatCurrency(Value))
        MsgBox("Desired House Matched")
    Else
        MsgBox("The House Doesn't Match the Desired Criteria")
    End If
End Sub

To understand how logical conjunction works, from a list of real estate properties, after selecting the house type, if you find a house that is a single family home, you put it in the list of considered properties:

Type of House House
The house is single family True

Logical Conjunction

If you find a house that is less than or equal to $550,000, you retain it:

Price Range Value
$550,000 True

For the current customer, you want a house to meet BOTH criteria. If the house is a town house, based on the request of our customer, its conditional value is false. If the house is less than $550,000, such as $485,000, the value of the Boolean Value is true:

Logical Conjunction

If

AND

If the house is a town house, based on the request of our customer, its conditional value is false. If the house is more than $550,000, the value of the Boolean Value is true. In logical conjunction, if one of the conditions is false, the result if false also. This can be illustrated as follows:

Type of House House Value Result
Town House $625,000 Town House AND $625,000
False False False

Suppose we find a single family home. The first condition is true for our customer. With the AND Boolean operator, if the first condition is true, then we consider the second criterion. Suppose that the house we are considering costs $750,500: the price is out of the customer's range. Therefore, the second condition is false. In the AND Boolean algebra, if the second condition is false, even if the first is true, the whole condition is false. This would produce the following table:

Type of House House Value Result
Single Family $750,500 Single Family AND $750,500
True False False

Suppose we find a townhouse that costs $420,000. Although the second condition is true, the first is false. In Boolean algebra, an AND operation is false if either condition is false:

Type of House House Value Result
Town House $420,000 Town House AND $420,000
False True False

If we find a single family home that costs $345,000, both conditions are true. In Boolean algebra, an AND operation is true if BOTH conditions are true. This can be illustrated as follows:

Type of House House Value Result
Single Family $345,000 Single Family AND $345,000
True True True

These four tables can be resumed as follows:

If Condition1 is If Condition2 is Condition1
AND
Condition2
False False False
False True False
True False False
True True True

As you can see, a logical conjunction is true only of BOTH conditions are true.

Combining Conjunctions

As seen above, the logical conjunction operator is used to combine two conditions. In some cases, you will need to combine more than two conditions. Imagine a customer wants to purchase a single family house that costs up to $450,000 with an indoor garage. This means that the house must fulfill these three requirements:

  1. The house is a single family home
  2. The house costs less than $450,001
  3. The house has an indoor garage

Here is the program that could be used to check these conditions:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Value As Double
    Dim IndoorGarageAnswer As Integer
    Dim Answer As String

    TypeOfHouse = "Unknown"

    Choice = _
        CInt(InputBox("Enter the type of house you want to purchase" _
             & vbCrLf & _
                  "1. Single Family" & vbCrLf & _
                  "2. Townhouse" & vbCrLf & _
                  "3. Condominium" & vbCrLf & vbCrLf & _
                  "You Choice? "))
    Value = CDbl(InputBox("Up to how much can you afford?"))

    TypeOfHouse = Choose(Choice, "Single Family", _
                        "Townhouse", _
                        "Condominium")

    IndoorGarageAnswer = _
            MsgBox("Does the house have an indoor garage (1=Yes/0=No)?", _
                   vbQuestion Or vbYesNo, _
                   "Real Estate")
    Answer = IIf(IndoorGarageAnswer = vbYes, "Yes", "No")

    If (TypeOfHouse = "Single Family") And _
       (Value <= 550000) And _
       (IndoorGarageAnswer = vbYes) Then
        MsgBox "Desired House Type:      " & vbTab & TypeOfHouse & vbCrLf & _
               "Maximum value afforded:  " & vbTab & _
               FormatCurrency(Value) & vbCrLf & _
               "House has indoor garage: " & vbTab & Answer
        MsgBox "Desired House Matched"
    Else
        MsgBox ("The House Doesn't Match the Desired Criteria")
    End If
End Sub

We saw that when two conditions are combined, the interpreter first checks the first condition, followed by the second. In the same way, if three conditions need to be considered, the interpreter evaluates the truthfulness of the first condition:

Type of House
A
Town House
False

If the first condition (or any condition) is false, the whole condition is false, regardless of the outcome of the other(s). If the first condition is true, then the second condition is evaluated for its truthfulness:

Type of House Property Value
A B
Single Family $655,000
True False

If the second condition is false, the whole combination is considered false:

A B A AND B
True False False

When evaluating three conditions, if either the first or the second is false, since the whole condition would become false, there is no reason to evaluate the third. If both the first and the second conditions are false, there is also no reason to evaluate the third condition. Only if the first two conditions are true will the third condition be evaluated whether it is true:

Type of House Property Value Indoor Garage
A B C
Single Family $425,650 None
True True False

The combination of these conditions in a logical conjunction can be written as A AND B AND C. If the third condition is false, the whole combination is considered false:

A B A AND B C A AND B AND C
True True True False False

From our discussion so far, the truth table of the combinations can be illustrated as follows:

A B C A AND B AND C
False Don't Care Don't Care False
True False Don't Care False
True True False False

The whole combination is true only if all three conditions are true. This can be illustrated as follows:

A B C A AND B AND C
False False False False
False False True False
True False False False
True False True False
False True False False
False True True False
True True False False
True True True True
 
 

Logical Disjunction: OR

 

Introduction

Our real estate company has single family homes, townhouses, and condominiums. All of the condos have only one level, also referred to as a story. Some of the single family homes have one story, some have two and some others have three levels. All townhouses have three levels.

Another customer wants to buy a home. The customer says that he primarily wants a condo, but if our real estate company doesn't have a condominium, that is, if the company has only houses, whatever it is, whether a house or a condo, it must have only one level (story) (due to an illness, the customer would not climb the stairs). When considering the properties of our company, we would proceed with these statements:

  1. The property is a condominium
  2. The property has one story

If we find a condo, since all of our condos have only one level, the criterion set by the customer is true. Even if we were considering another (type of) property, it wouldn't matter. This can be resumed in the following table:

Type of House House
Condominium True

The other properties would not be considered, especially if they have more than one story:

Number of Stories Value
3 False

We can show this operation as follows:

Condominium One Story Condominium or 1 Story
True False True

Creating a Logical Disjunction

To support "either or" conditions in the Visual Basic language, you use the Or operator. Here is an example:

Sub Exercise
    Dim TypeOfHouse As String
    Dim Choice As Integer
    Dim Stories As Integer
        
    TypeOfHouse = "Unknown"

    Choice = _
	  CInt(InputBox("Enter the type of house you want to purchase" & vbCrLf & _
                  "1. Single Family" & vbCrLf & _
                  "2. Townhouse" & vbCrLf & _
                  "3. Condominium" & vbCrLf & vbCrLf & _
                  "You Choice? ", "Real Estate", 1))

    TypeOfHouse = Choose(Choice, "Single Family", _
                                 "Townhouse", _
                                 "Condominium")
    Stories = CInt(InputBox("How many stories?", "Real Estate", 1))

    If Choice = 1 Or Stories = 1 Then
        MsgBox("Desired House Type:" & vbTab & TypeOfHouse & vbCrLf & _
               "Number of Stories:" & vbTab & vbTab & Stories)
        MsgBox("Desired House Matched")
    Else
        MsgBox("The House Doesn't Match the Desired Criteria")
    End If
End Sub

Here is an example of running the program:

Logical Disjunction

Logical Disjunction

Logical Disjunction

Logical Disjunction

As done for the And operator, to make a logical disjunction easy to read, you can include each statement in parentheses:

Sub Exercise
        . . . No Change

    If (Choice = 1) Or (Stories = 1) Then
        MsgBox ("Desired House Type:" & vbTab & TypeOfHouse & vbCrLf & _
               "Number of Stories:" & vbTab & vbTab & Stories)
        MsgBox ("Desired House Matched")
    Else
        MsgBox ("The House Doesn't Match the Desired Criteria")
    End If

End Sub

Suppose that, among the properties our real estate company has available, there is no condominium. In this case, we would then consider the other properties:

Type of House House
Single Family False

If we have a few single family homes, we would look for one that has only one story. Once we find one, our second criterion becomes true:

Type of House One Story Condominium OR 1 Story
False True True

This can be illustrated in the following run of the above program:

Or

Or

Or

If we find a condo and it is one story, both criteria are true. This can be illustrated in the following table:

Type of House One Story Condominium OR 1 Story
False True True
True True True

The following run of the program demonstrates this:

Or

Or

Or

A Boolean OR operation produces a false result only if BOTH conditions ARE FALSE:

If Condition1 is If Condition2 is Condition1 OR Condition2
False True True
True False True
True True True
False False False

Here is another example of running the program:

Or

Or

Combinations of Disjunctions

As opposed to evaluating only two conditions, you may face a situation that presents three of them and must consider a combination of more than two conditions. You would apply the same logical approach we reviewed for the logical conjunction, except that, in a group of logical disjunctions, if one of them is true, the whole statement becomes true.

 
   

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