GATE CSE 1988 | Question: 2vii

Question

Define the validity of a well-formed formula(wff)?

Comments

what does it mean?

Answer 1

Valid: A wff which is always true (tautology) is valid. i.e., its value is true for any set of assignment to its variables.

Satisfiable: A wff which is not a contradiction (always false) is satisfiable. It may be a tautology.

Comments

https://math.stackexchange.com/questions/258602/what-is-validity-and-satisfiability-in-a-propositional-statement

 

For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE.

In contrast, "a AND NOT a" is unsatisfiable.

(source : wikipedia)

Valid means tautology.

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Valid: A wff which is always true (tautology) is valid. i.e., its value is true for any set of assignment to its variables.

Satisfiable: A wff which is not a contradiction (always false) is satisfiable. It may be a tautology or contingency .

Tautology : Always True 

Contingency : Sometimes True Sometimes False Or In atleast one case it must be True or False

Answer 2

A well formed formula is valid means –

1. The conclusion is inferred from the premises.
2. The propositional expression is tautological implication.
3. The argument (an argument is sequence of propositional expressions followed by conclusion) proposed is valid.

Now let us consider the example and show if the argument is valid.

If it is raining Mr. Will will take an umbrella.

It is raining.

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Here p: It is raining, q: He will take an umbrella.

$((p \rightarrow q) \wedge (p)) \rightarrow p$

The above written expression is tautological implication. Hence we can say that the argument is valid.

Answer 3

Valid = Always True.

Consistent/ Satisfiable = We can make the wff true (meaning there can be False results too)