Question
Download Solution PDFConsider 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 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe 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
Key Points
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.
Additional Information
- 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.
Last updated on Jun 12, 2025
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