What is the difference between Well-formed formula and a preposition in propositional logic

Question

What is the exact difference between Well-formed formula and a proposition in propositional logic?

There's really not much given about Wff in my book.

My book says: "Propositions are also called sentences or statements. Another term formulae or well-formed formulae also refer to the same. That is, we may also call Well formed formula to refer to a proposition". Does that mean they both are the exact same thing?

Answer 1

Proposition: A statement which is true or false, easy for people to read but hard to manipulate using logical equivalences

WFF: An accurate logical statement which is true or false, there should be an official rigorus definition in your textbook. There are 4 rules they must follow. Harder for humans to read but much more precise and easier to manipulate

Example:

• Proposition : All men are mortal
• WFF: Let P be the set of people, M(x) denote x is a man and S(x) denote x is mortal Then for all x in P M(x) -> S(x)

Answer 2

It is most likely that there is a typo in the book. In the quote Propositions are also called sentences or statements. Another term formulae or well-formed formulae also refer to the same. That is, we may also call Well formed formula to refer to a preposition, the word "preposition" should be "proposition".

Answer 3

Proposition :- A statement which is either true or false,but not both.

Propositional Form (necessary to understand Well Formed Formula) :- An assertion which contains at least one propositional variable.

Well Formed Formula :-A propositional form satisfying the following rules and any Wff(Well Formed Formula) can be derived using these rules:-

1. If P is a propositional variable then it is a wff.
2. If P is a propositional variable,then ~P is a wff.
3. If P and Q are two wffs then,(A and B),(A or B),(A implies B),(A is equivalent to B) are all wffs.