Answer to Question #171757 in Discrete Mathematics for markmarbella

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. (15 points)

3. Show, by the use of the truth table (truth matrix), that the  is a contradiction. (15 points)

• <i class="add" style="width: 20px; height: 20px; display: inline-block; vertical-align: top; position: relative; overflow: hidden; margin: 0px 6px 0px 0px;"></i>Prepare answer

Answer 1

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:

The total statement is not always true, not always false. So this statement is contingency.