Kenneth Rosen Edition 7 Exercise 1.2 Question 3 (Page No. 22)

Question

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

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.”

Answer 1

P only if Q means (P$\rightarrow$Q). 

So, answer is g$\rightarrow$(r$\wedge\neg$m$\wedge\neg$b). 

Answer 2

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.”

Now no money owe=∿m

no overdue of book=∿b

so

(r   ^ (∿m )^ (∿b))---->g

Comments

yes only if conditions i put in first! is mine correct?

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why can't it be : g <=> (r ^ ~m ^ ~ b) ?

because it can be written as ->  you can graduate if and 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.

for completing the graduation it is a necessary and sufficient condition

it can also be written as: if you have completed the requirements of your major and you do not  owe money to university and you do not  have an overdue then you can graduate .  if we this sentence is p-> q here then q-> p is also possible , y definition then it is p <=> q.

I am confused about the answer please share your thoughts about this.

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@Shashikant Dwivedi 1

in question given only if you can't written as if and only if because both have different meaning.