Question

Consider the following two well-formed formulas in prepositional logic.

F1: \(P \Longrightarrow \neg \;P\)

F2: \((P \Longrightarrow \neg \;P) \;\vee\; (\neg \; P \Longrightarrow P)\)

Which of the following statements is correct ? 

1. F1 is Satisfiable, F2 is valid
2. Fl is unsatisfiable, F2 is Satisfiable
3. F1 is unsatisfiable, F2 is valid
4. Fl and F2 both are Satisfiable

Answer 1

Correct Answer - Option 1 : F1 is Satisfiable, F2 is valid

The correct answer is option 1.

CONCEPT:

Valid: If for all the combinations of variables, the expression returns true then it is valid.

Satisfiable: If there exists at least one combination of variable which return true then it is satisfiable

F1: It is Satisfiable.

P	¬P	P⇒¬P
T	F	F
F	T	T

F2: It is valid

P	¬P	P⇒¬P	¬P⇒P	(P⇒¬P)∨(¬P⇒P)
T	F	F	T	T
F	T	T	F	T

∴ Hence the correct answer is F1 is Satisfiable, F2 is valid.

• A proposition P is a tautology if it is true under all circumstances. It means it contains only TRUE in the final column of its truth table.
• A statement that is always false is known as a contradiction.
• A statement that can be either true or false depending on the truth values of its variables is called a contingency.