Question

You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book. Express your answer in terms of g: “You can graduate,” m: “You owe money to the university,” r: “You have completed the requirements of your major,” and b: “You have an overdue library book.”

Short answer

The logical proposition of the given statement is determined as,

g\( \to \)(r˄(~m)˄(~b)).

Step-by-step solution

Introduction to the Concept

The statement is made up of conditionals and conjunctions.

$$\begin{gathered} \vee \to \mathrm{or} \\ \wedge \to \mathrm{and} \\ \underset{}{\to }:\mathrm{only}\mathrm{if} \end{gathered}$$

Solution Explanation

The given statements are,

g: You can graduate

m:You owe money to the university

r: You have completed the requirements of your major

b:You have an overdue library book

“You can graduate only if you have completed the requirements of your major“says the statement.

“You do not owe money to the university and you do not have an overdue library book”.

The logical proposition statement is given as g\( \to \)(r˄(~m)˄(~b)) .