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## Here's the Solution to this Question

(b).

Let $P\left(x\right)=x\:$ cares about the ocean pollution, $C\left(x\right)=x$ is in the class, $\:W\left(x\right)=x$ enjoys whale watching.

Then the premises are $\forall x\left(W\left(x\right)\rightarrow P\left(x\right)\right),\:\exists x\left(W\left(x\right)\wedge C\left(x\right)\right)$ and the conclusion is

$\exists \:x\left(C\left(x\right)\wedge \:P\left(x\right)\right)$

The following steps can be used to establish the conclusion from the premises

Step : Reason

1. $\exists x\left(W\left(x\right)\wedge \:\:C\left(x\right)\right)$ : Premise
2. $\forall x\left(W\left(x\right)\rightarrow P\left(x\right)\right)\:$ : Premise

Use the rule of inference existential instantiation $\exists xP\left(x\right)\Rightarrow P\left(c\right)\:for\:\exists x\left(W\left(x\right)\wedge C\left(x\right)\right)$

3.$W\left(y\right)\wedge C\left(y\right)$ : Existential Instantiation

Apply simplification of 3.

4.$W\left(y\right)$ : Simplification of 3

Use the rule of inference universal instantiation $\forall xP\left(x\right)\Rightarrow P\left(c\right)\:for\:\forall x\left(W\left(x\right)\rightarrow P\left(x\right)\right)$

5.$W\left(y\right)\rightarrow P\left(y\right)$ : Universal instantiation of 2.

Apply modulus ponens using steps 4 and 5.

6.$P\left(y\right)$ : Modulus ponens from 4 and 5.

Apply simplification of 3.

7.$C\left(y\right)$ : Simplification of 3.

Apply conjunction using steps 6 and 7 and then apply existential generalization to the final step to get the conclusion.

8.$C\left(y\right)\wedge P\left(y\right)$ : Conjunction from 6 and 7.

9.$\exists x\left(C\left(x\right)\wedge P\left(x\right)\right)$ : Existential generalization of 8.

Therefore, the conclusion is that, there is a person in this class who cares about ocean pollution.