Well formulated formula?

Logic Level 1

According to propositional logic , which of the following is not a well formulated formula?

(1): ( $A \wedge B) \to (C \vee D)$
(2): ( $A \neg B) \to (C \vee D)$
(3): ( $A \leftrightarrow B) \to (\neg D)$

None of them 3 1 2 and 3 All of them 1 and 2 2 1 and 3

1 solution

Geoff Pilling
Jan 29, 2017

A proposition is called a "well formed formula" (or wff) if it is constructed with the following set of rules:

Any atomic proposition is a well formed formula.
If $A$ is a well formed formula, then $\neg A$ is also a well formed formula.
If $A$ and $B$ are well formed formulae, then $(A \wedge B)$ is also a well formed formula.
If $A$ and $B$ are well formed formulae, then $(A \vee B)$ is also a well formed formula.
If $A$ and $B$ are well formed formulae, then $(A \to B)$ is also a well formed formula.
If $A$ and $B$ are well formed formulae, then $(A \leftrightarrow B)$ is also a well formed formula. $_\square$
Unless constructed using only 1-6 above, then a proposition isn't a well formed formula.

In the three choices above, $1$ and $3$ can be constructed using the above requirements for a wff. However, $2$ is nonsense, since $\neg$ is a unary operator so $A \neg B$ is nonsense.

Therefore, $\boxed2$ is the right answer.

None of them are well formed formula because the outer parenthesis is missing - ((A∧B)→(C∨D)) is a well formed formula but (A∧B)→(C∨D) isn't

tor mata - 6 months ago

2 is the right answer but in the exercise 1 and 3 is the right answer

Miquel Seixas da Paixao - 1 month, 3 weeks ago

Well formulated formula?

1 solution

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