Answer to Question #269377 in Discrete Mathematics for Forhed

Question

P = I pass this class

G = I go to class every day.

H = I do all the homework exercises.

Translate the following sentences into propositional logic.

(1) Students will not pass this class unless they go to class every day and do all of the 

homework exercises.

 

(2) Either going to classes every day or doing all the homework exercises is necessary 

for passing this class for students.

(3) There is no student in the class who goes to classes every day and does all the 

homework exercises but will not pass this class.(4) To pass in the class it is necessary and sufficient to go to classes every day or do all 

the homework exercises.

 

(5) Either go to classes every day or do all the homework exercises but both is not 

required if students wants to pass the

Answer 1

Let $x\in X$ , where X - the set of all students

(1) $\forall x:$ $p(x)\to(g(x)\land h(x))$

(2) $\forall x:p(x)\to(g(x)\lor h(x))$

(3) $\forall x:(g(x)\land h(x))\to p(x)$

(4) $\forall x:p(x)\leftrightarrow (g(x)\lor h(x))$

(5) $\forall x:((g(x)⊕h(x)) \to p(x)$