PREDICATES AND QUANTIFIERS

• Predicate- true,false (proposition that contain variable)

        P(x)= X>0

• Quantification express the extent to which a predicate is true over a 

         range of elements

         x>0

         x= true

         x=false

• Universal Quantifiers

        P(x) is true for every x in the universe of 
        discourse.

        "xP(x)

        

        Eg:U={1,2,3}

        "xP(x) óP(1) Ù P(2) Ù P(3)

• Existensial Quantifiers

        P(x) is true for some x in the universe of 
        discourse

        $xP(x)

       

        ‘There is an x such that P(x),’For some x,
         P(x)’,’For at least one x,

   

        P(x)’,’I can find an x such that P(x)’.

       

       Eg: U={1,2,3}

       $xP(x)óP(1) Ú P(2) Ú P(3)

• Unique Existensial

        P(x) is true for one and only are x in the 
        universe of discourse

       $!xP(x)

        

       ‘There is a unique x such that P(x),’
        There is one and only one x such

        that P(x)’,’One can find only 
        one x such that P(x).’

        

        Eg:U={1,2,3}

        

        Truth Table:

        P(1)   P(2)   P(3)   $!xP(x)

0       0       0       0

0       0       1       1

0       1       0       1

0       1       1       0

1       0       0       1

1       0       1       0

1       1       0       0

1       1       1       0




EXAMPLE OF APPLICATION IN LIFE:

UNIVERSAL

EXISTENSIAL

UNIQUE