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](https://tex.z-dn.net/?f=p%5Es)
Through parentheses or negation, deny the whole logical expression. e.g.
![\to \sim p^s](https://tex.z-dn.net/?f=%5Cto%20%5Csim%20p%5Es)
by using the rule of DeMorgan's:
![\to \sim p \ v \ \sim s \\](https://tex.z-dn.net/?f=%5Cto%20%5Csim%20p%20%5C%20v%20%20%5C%20%5Csim%20s%20%5C%5C)
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}.](https://tex.z-dn.net/?f=%5Ctext%7BThe%20applicant%20not%20has%20written%20permission%20from%20his%20parents%20or%20is%20at%20most%2015%20years%20old%7D.)
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](https://tex.z-dn.net/?f=p%20%5C%20v%20%5C%20e)
through brackets or negation, refute the entire logical expression.
![\to \sim (p\ v \ e)](https://tex.z-dn.net/?f=%5Cto%20%5Csim%20%28p%5C%20%20v%20%5C%20e%29)
Apply DeMorgan's law:
![\to \sim p ^ {\sim e}](https://tex.z-dn.net/?f=%5Cto%20%20%5Csim%20p%20%5E%20%7B%5Csim%20e%7D)
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}.](https://tex.z-dn.net/?f=%5Ctext%7BThe%20applicant%20not%20has%20written%20permission%20from%20his%20parents%20and%20is%20at%20most%2017%20years%20old%7D.)