24 ~ Theory of Computer Science
TABLE 1.15 Rules of Inference for Addition and
Deletion of Quantifiers
RI 13 : Universal instantiation
'ix P(x)
~
c is some element of the universe.
RI,4 : Existential instantiation
?:.xP(x)
. P(c)
c is some element for which P(c) is true.
Rl 1s : Universal generalization
P(x)
'ix P(x)
x should not be free in any of the given premises.
- - - - - ~. ..~--RI., 6
Existential generalization
P(c)
·. .=x P(x)
c is some element of the universe.
.EXAMPLE 1.22
Discuss the validity of the following argument:
All graduates are educated.
Ram is a graduate.
Therefore. Ram is educated.
Solution
Let G(x) denote 'x is a graduate'.
Let E(x) denote 'x is educated'.
Let R denote 'Ram'.
So the premises are (i) 'If.r (G(x) =} E(x)) and (ii) G(R). The conclusion is E(R).
'lfx (G(x) =} E(x))
Premise (i)
G(R) =} E(R)
Universal instantiation RI 13
G(R)
Premise (ii)
:. E(R)
Modus ponens RI 4
Thus the conclusion is valid.
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