Answer to Question #170641 in Discrete Mathematics for Usui Takumi

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 -p → (q + r) and q→ (p V r) are logically equivalent.

3. Show, by the use of the truth table (truth matrix), that the (pvq)v [(-p)^(q)] is a contradiction.

Answer 1

1.

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

2.

Since truth tables of the statements are not identical, the given statements are not equivalent.

3.

Since the statement is not always false, it is not contradiction.