Missing Part of Question
Explain which rules of inference are used in the above
Answer:
Universal instantiation, Modus ponens and Existential generalization
Explanation:
Splitting the Statement into two, we have
"Doug knows how to write program is Java"
and
"Doug can get a high paying job"
Represent Doug with x. Then the statements is rewritten as
P(x) = "x knows how to write program is Java"
and
Q(x) = "x can get a high paying job"
In logic, A premise is a statement in an argument that provides reason or support for the conclusion.
So, Statement 1 can be written as
1. P(x) ---- Premise
Then, we have
2. Vx(P(x) --> Q(x)) -- Premise. This mean that P(x) for all values in the domain.
The universal instantiation of (2) leads to
3. P(Doug) --> Q(Doug)
The modus ponens of the above gives
4. Q(Doug)
The existential generalisation from above gives
5. ƎxQ(x)
Which means someone in this class can get a high paying job.
PS:
Universal Instantiation is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class; it is represented by VxP(x).
Existential Generalisation is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition.
It is represented as ƎxP(x)