Showing Valid Predicate Inference Examples 1

In this class, We discuss Showing Valid Predicate Inference Examples 1.

The reader should have prior knowledge of universal generalization. Click Here.

Example:

Show that ∃x(M(x)) logically follows from the premises (x)(H(x) -> M(x)) and ∃x(H(x))

The diagram below shows the derivation

Example:

∃xP(x) ∧ ∃xQ(x) => ∃x(P(x) ∧ Q(x))

The below diagram shows the derivation.

In this case, we can not derive.

The variable y is a free variable in the derivation, so we can not use it again for Q.

It is not possible to derive the above.

Example:

∃x(P(x) ∧ Q(x)) => ∃xP(x) ∧ ∃xQ(x)

This example is an assignment for the reader.