Question

To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service. Express your answer in terms of w: “You can use the wireless network in the airport,” d: “You pay the daily fee,” and s: “You are a subscriber to the service.”

Short answer

The logical proposition of the given statement is determined as, $\mathbf{w}\mathbf{\to }\mathbf{(}\mathbf{d}\mathbf{\vee }\mathbf{s}\mathbf{)}$.

Step-by-step solution

Introduction to the Concept

The logical sign for 'if__then' is '' and for 'or' the logical symbol is '$\mathbf{\vee }$’.

Solution Explanation

The given statements are,

w: You can use the wireless network in the airport

d: You pay the daily fee

s: You are a subscriber to the service

The assertion is

To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service.

So, in propositional logic, the statement is $\mathbf{w}\mathbf{\to }\mathbf{(}\mathbf{d}\mathbf{\vee }\mathbf{s}\mathbf{)}$.