6 votes 6 votes Let $\alpha, \beta $ be two propositional formulas. Which of the following assertions is true? $\alpha \models \beta$ if and only if the sentence $(\alpha \wedge \neg \beta)$ is unsatisfiable. If $\alpha\models \gamma $ or $\beta \models \gamma $ (or both) then $(\alpha \wedge \beta)\models \gamma $ If $(\alpha \wedge \beta)\models \gamma $ then $\alpha \models \gamma$ or $\beta \models \gamma $ (or both). If $\alpha \models(\beta \vee \gamma)$ then $\alpha \models \beta $ or $\alpha \models \gamma $ (or both). Mathematical Logic goclasses_wq5 goclasses mathematical-logic propositional-logic multiple-selects 2-marks + – GO Classes asked Mar 30, 2022 • retagged Apr 26, 2022 by Lakshman Bhaiya GO Classes 910 views answer comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments JAINchiNMay commented Oct 9, 2022 reply Follow Share unsatisfiable and negation are same? according to me if in truth table, even if only one entry is not equal then it is unsatisfiable in the video solution sir is using the both terms as same can someone explain 0 votes 0 votes Swapnil Sah commented Apr 12, 2023 i edited by Swapnil Sah Apr 12, 2023 reply Follow Share @Deepak Poonia Sir while making the rhs false in c,d option why are we not making false in the same row.C:to make the rhs false (alpha->gamma) is tautology or (beta->gamma) is tautology.here the "or" is a connective (or not).if not who to figure out;I watched the video but , i am still not getting. 0 votes 0 votes Deepak Poonia commented Apr 14, 2023 reply Follow Share @Swapnil Sah Let the renaming of the propositional formulas, $\alpha = A, \beta = B, \gamma = C.$ Option C says “If $ [ (A \wedge B \rightarrow C)$ is a Tautology] then [ $A \rightarrow C$ is Tautology OR $B \rightarrow C$ is Tautology] ” Now, Let $P,Q$ be two propositional variables (i.e. Atomic Propositions). Let: $A = P, B = P’, C = Q \wedge Q’ $ You can see that, using these formulas $A,B,C$, Option C is false. (Try to create the Truth Table & See) To make “$M$ is tautology OR $N$ is tautology” false, we need to show that it is possible that “Neither M, Not N are Tautology”. 2 votes 2 votes Please log in or register to add a comment.
0 votes 0 votes Update: C and D are not true. I solve this for propositional expressions, but these are inferences. If options C and D are tautology then the assertions are true. Option C: Option D: neel19 answered Mar 31, 2022 • edited Mar 31, 2022 by neel19 neel19 comment Share Follow See 1 comment See all 1 1 comment reply shadymademe commented Apr 3, 2022 reply Follow Share alpha, beta, and gamma are not atomic proposition, these are propositional formulae(on unknown variables). You can take all possible combinations of truth value and solve it like this because you can’t say for sure what were the truth values of those unknown variables. 1 votes 1 votes Please log in or register to add a comment.
