31 votes 31 votes Consider two well-formed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable Mathematical Logic gatecse-2001 mathematical-logic easy propositional-logic + – Kathleen asked Sep 14, 2014 • edited Jun 20, 2017 by Silpa Kathleen 9.1k views answer comment Share Follow See all 9 Comments See all 9 9 Comments reply Show 6 previous comments nocturnal123 commented Sep 28, 2021 reply Follow Share If this question would be MSQ, then option A) and D), both are correct. 4 votes 4 votes sukesh_reddy commented Dec 7, 2022 reply Follow Share I too think of the same think because a tautology is also satisfiable.. can any one correct me if i am wrong … My reasoning is the satisfiable wants at least one input combination for which the output is true .. and tautology give output true for all input combination of inputs .. 1 votes 1 votes ritiksri8 commented Mar 9 reply Follow Share Well we can solve this easily by the case method or by the boolean algebra 0 votes 0 votes Please log in or register to add a comment.
–1 votes –1 votes I can see both are satisfiable i wl go for option b Bhagirathi answered Sep 21, 2014 Bhagirathi comment Share Follow See all 5 Comments See all 5 5 Comments reply Arjun commented Sep 21, 2014 reply Follow Share If both are satisfiable (d) must be the answer rt? Also, isn't F2 valid making (a) a better answer? 4 votes 4 votes Bhagirathi commented Sep 21, 2014 reply Follow Share What is a valid argument? I dont know plz explain i know the satisfiable only 0 votes 0 votes Arjun commented Sep 21, 2014 reply Follow Share valid means always true. That is, whatever be the values assigned to the variables, the formula returns true. eg. $p\vee \neg p$ 6 votes 6 votes Bhagirathi commented Sep 21, 2014 reply Follow Share Then what is your opinion about this which is the most appropriate 0 votes 0 votes Arjun commented Sep 21, 2014 reply Follow Share (a) is the most appropriate. 12 votes 12 votes Please log in or register to add a comment.