Explain the 4 rules of inference for quantified statements.

1. Universal Instantiation:

      If the proposition of the form ∀xP(x) is true then it can be dropped down to get   

     P(c) true, for an arbitrary c. this can be written as,

     ∀xP(x)

     ∴P(c) for all c

eg: “Every student in this class read Math”, “Ram is in this classs”

    ∴”Ram reads Math”.

2.  Universal Generalization:

      If all the instances of c makes P(c) true then we can say ∀xP(x) is true. This is           written as,

P(c) for all c

 ∴∀xP(x)

3.   Existential Instantiation:

If the proposition of the form ∃xP(x) is true there is an element c in the universal set such that P(c) is true. This can be written as,

∃xP(x)

∴P(c) for some specific c

4.  Existential Generalization:

If at least one element c from the universal set makes P(c) true then we can say ∃xP(x) is true. This is written as,

P(c) for some c

∴∃xP(x)