For this arguments, explain which rules of inference are used for each step. Same body in this class enjoys whole watching. Every person who enjoys whole watching cares about ocean pollution. Therefore, there is a person in this class who cares about ocean pollution.
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(b).
Let cares about the ocean pollution, is in the class, enjoys whale watching.
Then the premises are and the conclusion is
The following steps can be used to establish the conclusion from the premises
Step : Reason
- : Premise
- : Premise
Use the rule of inference existential instantiation
3. : Existential Instantiation
Apply simplification of 3.
4. : Simplification of 3
Use the rule of inference universal instantiation
5. : Universal instantiation of 2.
Apply modulus ponens using steps 4 and 5.
6. : Modulus ponens from 4 and 5.
Apply simplification of 3.
7. : Simplification of 3.
Apply conjunction using steps 6 and 7 and then apply existential generalization to the final step to get the conclusion.
8. : Conjunction from 6 and 7.
9. : Existential generalization of 8.
Therefore, the conclusion is that, there is a person in this class who cares about ocean pollution.