Answer to Question #171424 in Discrete Mathematics for Mra

Question

1. Given the following:

• g: "You can graduate."
• m: "You owe money to the college."
• r: "You have completed the requirements of your major."
• b: "You have an overdue book."

Translate "You can graduate only if you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book." into a propositional logic.

2. Show that  are logically equivalent. 

3. Show, by the use of the truth table (truth matrix), that the  is a tautology.

Answer 1

$g\iff (r\land \neg m \land \neg b)$

2.Statements (You can graduate) and (you have completed the requirements of your major, you do not owe money to the college, and you do not have an overdue book) are equivalent, because there is "only if" condition between them; and result is true if both statement are true, or both statements are false.

3.Truth table: