Kenneth Rosen Edition 7 Exercise 1.2 Question 4 (Page No. 22)

Question

Translate the given statement into propositional logic using the propositions provided.
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.”

Answer 1

∿s ⟶ (w⟶d)

Here (w⟶d) means "If you want to use the wireless network in the airport then you must pay daily fee".

Let P = (w⟶d)

So (~s⟶P) means P unless ~(~s) as we  (p ⟶ q) means q unless ∿p.

So it means "If you want to use the wireless network in the airport then you must pay daily fee unless you are a subscriber to the service."

Comments

(Or) we can also write it as :-

$(w \; \wedge \sim s) \rightarrow d$

$\equiv \sim(w \wedge \sim s) \vee d$

$\equiv \sim w \vee  s \vee d$

$\equiv w \rightarrow (s \vee d)$ which is also equivalent to the expression given in the answer.

Answer 2

w -> ( d or s )

Answer 3

(w -> d) ^ - s

Answer 4

IF(NOT A SUBSCRIBER)

{

IF(YOU PAY)

THEN

U CAN USE

}

SO FROM THE PROPOSITIONS ANS WILL BE

(- s^d)→w=(NOT S AND D)→W