Question

Translate each English sentence into a logical expression using the propositional variables defined below. Then negate the entire logical expression using parentheses and the negation operation. Apply De Morgan's law to the resulting expression and translate the final logical expression back into English. p: the applicant has written permission from his parents e: the applicant is at least 18 years old s: the applicant is at least 16 years old (a) The applicant has written permission from his parents and is at least 16 years old. (b) The applicant has written permission from his parents or is at least 18 years old.

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In point a:

If the applicant's parents provide written permission and are 16 years old or older.  

Solution:  

Logical term: $p^s$

Through parentheses or negation, deny the whole logical expression. e.g.  

$\to \sim p^s$

by using the rule of DeMorgan's:  

$\to \sim p \ v \ \sim s$

The following logical expression is the English phrase:  

$\text{The applicant not has written permission from his parents or is at most 15 years old}.$

In point b:

A parent of the applicant has submitted approved permission or the age of 18 years or older.

Logical expression:$p \ v \ e$

through brackets or negation, refute the entire logical expression.  

$\to \sim (p\ v \ e)$

Apply DeMorgan's law:

$\to \sim p ^ {\sim e}$

by using the rule of DeMorgan's:  

The following logical expression is the English phrase:  

$\text{The applicant not has written permission from his parents and is at most 17 years old}.$