Universal Existential Specification or Instantiation || Lesson 34 || Discrete Math & Graph Theory ||

Universal Existential Specification or Instantiation
In this class, We discuss Universal Existential Specification or Instantiation.
The reader should have prior knowledge of free and bound variables. Click Here.
Universal specification or instantiation
∀x(A(x)) from this one can conclude A(y).
A(x) is true for all x, then it is true for A(y)
y is a subject.
The above statement can be written as ∀x(A(x)) =gt A(y).
∀x(A(x)) is tautologically implies A(y).
Existential specification or instantiation
∃x(A(x)) one can conclude A(y)
If ∃x(A(x)) is true, it means at least one subject A(x) is true.
We can say A(y) is true.
Conditions:
y should not be a free variable in any of the premises
y should not be a free variable in any of the prior steps of derivation.
Existential Generalization:
A(x) =gt ∃y(A(y))
A(x) is true means at least true for one subject so that we can conclude for ∃y(A(y))

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