11 votes 11 votes Which of the following statements is true? The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\rightarrow S$ is valid. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is consistent. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent. Mathematical Logic goclasses2025_cs_wq2 goclasses mathematical-logic propositional-logic 1-mark + – GO Classes asked Mar 26, 2023 • edited Mar 26 by shadymademe GO Classes 1.2k views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply Deepak Poonia commented Mar 28, 2023 reply Follow Share Detailed Video Solution: Weekly Quiz 5 Detailed Video Solutions 0 votes 0 votes Ajay_22 commented Mar 29, 2023 reply Follow Share @Deepak Poonia sir Consistent <=> Valid Is it correct ? 0 votes 0 votes Deepak Poonia commented Mar 29, 2023 reply Follow Share Consistent = Satisfiable. 0 votes 0 votes Shubhamishere commented May 17, 2023 reply Follow Share inconsistent = unsatisfiable? 0 votes 0 votes Suryaputra_Karn commented May 17, 2023 reply Follow Share yes 1 votes 1 votes Srken commented Jul 19, 2023 reply Follow Share So,If this question was asked as Multiple select question (MSQ) then we can choose Option A,B,C right.. 1 votes 1 votes Deepak Poonia commented Jul 19, 2023 reply Follow Share @Srken, No. Only B is correct. All the options are “if and only if” statements. Video Solution: https://youtu.be/LgAocElBy8U 0 votes 0 votes ayushyadav05 commented Mar 13 reply Follow Share in option D if we have valid in valid then it is also true right ??? 0 votes 0 votes Please log in or register to add a comment.
Best answer 6 votes 6 votes The sentence $S$ is a logical consequence of $S_{1}, ... S_{n}$ if and only if $S_{1} \wedge S_{2} ... \wedge S_{n} \rightarrow S$ is Tautology or Valid, hence option B is correct. sankalps answered Mar 26, 2023 • selected Mar 29, 2023 by Deepak Poonia sankalps comment Share Follow See all 2 Comments See all 2 2 Comments reply chokostar commented Mar 26, 2023 reply Follow Share But should we consider “if and only if” to be important here? If so then the sentence would change like, If S is a logical consequence of S1, … Sn, then S1 ^ .. Sn → S is valid (or tautology). @Deepak Poonia 1 votes 1 votes KG commented Mar 27, 2023 reply Follow Share Definitions are always ‘iff’ statements. And option B is the definition of Valid Argument. 3 votes 3 votes Please log in or register to add a comment.
1 votes 1 votes Logical consequence is a concept which describes the relationship between statements that hold TRUE/VALID when one statement logically follows from one or more statements (Source: Wikipedia) himanshud2611 answered Mar 27, 2023 himanshud2611 comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes all tautologies are valid but all valid are not tautology keerthanavu answered Apr 18, 2023 keerthanavu comment Share Follow See all 2 Comments See all 2 2 Comments reply ayush_27 commented May 9, 2023 reply Follow Share I could not understand, can you please elaborate with an example? 0 votes 0 votes Srken commented Jul 19, 2023 reply Follow Share All tautologies are valid arguments and it’s vice versa . If an argument is valid then it's definitely Tautology that’s what we prove in logical arguments right. 0 votes 0 votes Please log in or register to add a comment.
