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 934 views answer comment Share Follow See all 16 Comments See all 16 16 Comments reply Vishu Nair commented Mar 30, 2022 i reshown by Vishu Nair Mar 31, 2022 reply Follow Share It's not just A,B only as given in quiz solution. I think C is also correct. Could you please update in the solutions, if applicable? 0 votes 0 votes neel19 commented Mar 31, 2022 reply Follow Share I think all are correct. 0 votes 0 votes Vishu Nair commented Mar 31, 2022 i reshown by Vishu Nair Mar 31, 2022 reply Follow Share D is not correct I solved again. Got A,B and C this time as well. Let's see 0 votes 0 votes neel19 commented Mar 31, 2022 reply Follow Share Can you check the answer if there is anything wrong with it? I think D is correct. 0 votes 0 votes neel19 commented Mar 31, 2022 reply Follow Share Please don’t hide comments. Other users won’t be able to know what was the context. My above comments now doesn’t make any sense. 0 votes 0 votes Vishu Nair commented Mar 31, 2022 reply Follow Share Ok, I was checking to be sure, will reshow all comments in a couple of minutes. 0 votes 0 votes Deepak Poonia commented Mar 31, 2022 reply Follow Share Detailed Video Solution: https://youtu.be/nclBhBmtz2g?t=4465 0 votes 0 votes Vishu Nair commented Mar 31, 2022 i edited by Vishu Nair Mar 31, 2022 reply Follow Share Thank you @Deepak Poonia sir. But the quiz is active and few have taken it. I think, solutions could be released for viewing after the quiz is closed. Sorry if I have misunderstood anything. 0 votes 0 votes sidd_07 commented Apr 1, 2022 reply Follow Share DOUBT in WQ5 Q12 Opt C, I am trying to solve by simplification and I reached a similir result in LHS of implication and RHS of Implication. Please let me know what I’m doing wrong. 0 votes 0 votes neel19 commented Apr 1, 2022 reply Follow Share These are not propositional statements. These are inferences. You cannot simply them like this. Option C says, If the inference on the LHS is true then the inference alpha → gamma or beta → gamma is true. But as sir explained in the YouTube solution, that’s not the case. The inference on LHS can be made tautology, and simultaneously the inferences on the consequence side are falsiable, and because of that implication doesn’t hold. That’s why C isn’t correct. Check the youtube solution for more info. There it's explained in detailed manner. 1 votes 1 votes sidd_07 commented Apr 2, 2022 reply Follow Share A infers to B means A → B is tautology, then why can’t we simplify them. I have watched YT video. I just want to know what is the mistake in my approach. Thanks. 0 votes 0 votes shishir__roy commented Apr 3, 2022 i edited by shishir__roy Apr 3, 2022 reply Follow Share That OR operation, in question means that -(alpha -> gamma) is tautology or (beta -> gamma) is tautology (or both).And what you're doing is -((alpha -> gamma) or (beta -> gamma)) is tautology. 2 votes 2 votes Deepak Poonia commented Apr 20, 2022 reply Follow Share Detailed Video Solution 1 votes 1 votes 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.