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spaghetti3451
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Homework Statement
Consider the following statements.
All engineers either like computer or like power tools. All engineers who like computers
like video games. All engineers who like power tools like camping out. Some engineers
like literature.
Based on these given statements, show that you can make the following inferences. Show
all steps in your work.
There is at least one engineer who likes video games and literature.
Homework Equations
The Attempt at a Solution
Let E(x) be the proposition 'x is an engineer,'
Let C(x) be the proposition 'x likes computer,'
Let P(x) be the proposition 'x likes power tool,'
Let V(x) be the proposition 'x likes video games,'
Let O(x) be the proposition 'x likes camping out,'
Let L(x) be the proposition 'x likes literature,'
where x is the domain of all people.
Steps and corresponding reasons:
1. [itex]\forall[/itex]x E(x) → C(x) [itex]\vee[/itex] P(x) premise
2. E(a) → C(a) [itex]\vee[/itex] P(a) universal generalisation
3. [itex]\forall[/itex]x (E(x)[itex]\wedge[/itex]C(x)) → V(x) premise
4. (E(a)[itex]\wedge[/itex]C(a)) → V(a) universal generalisation
5. [itex]\forall[/itex]x (E(x)[itex]\wedge[/itex]P(x)) → O(x) premise
6. (E(a)[itex]\wedge[/itex]P(a)) → O(a) universal generalisation
7. ∃x E(x)[itex]\wedge[/itex]L(x) premise
8. E(a)[itex]\wedge[/itex]L(a) existential generalisation
I'm not sure about the statements for universal and existential generalisation, i.e. if they should all refer to the same a.