Answer to Question #262958 in Discrete Mathematics for Arbaz

Question

Asim, a student in this class, knows how to write programs in Java. Everyone who knows how to write programs in Java can get a high-paying job. Therefore, someone in this class can get a high-paying job

Answer 1

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