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## Here's the Solution to this Question

Part a

Let p(x) be "x is a student", q(x) means "x knows how to code in java", r(x) means "x can get a high-paying job"

We have next statements: $\exists x(p(x)\land q(x))$ , $\forall x(q(x)\to r(x))$

we have to check whether the statement $\exists x:(p(x)\to r(x))$ is true

lets assume it is false, then $\forall x: (p(x)\to \lnot r(x))$ , but from the first two statements we can tell that b

$\exists x(p(x)\to r(x))$ . So, we came to contradiction, which means our statement is false, which means there is someone in the class who can get a high-paying job

Part b

Let P(x) = x cares about ocean pollution, C(x) = x is in the class, W(x)= x enjoys whale watching. Then the premises are $\forall x(W(x) \to P(x)), \exists x(W(x)\land C(x))$ and the conclusion is $\exists x(C(x)\land P(x))$

Part c

Let C(x) = x is in the class, P(x) = x owns a personal computer, W(x). x can use a word processing program, and Z = Asim.

Then the premises are $\forall x(C(x) \to P(x)), \forall x(P(x) \to W(x)),C(Z)$ , and the conclusion is W(Z).

Part d

Let J (x) = x lives in Karach, 0 (x) = x lives within 50 miles of the ocean, S(x) = x has seen the Ocean. Then the premises are $\forall x(J (x \to 0(x)), \exists x(J(x) \land ¬ S(x))$ , and the conclusion is $\exists x(O(x) \land ¬ S(x))$