0 votes 0 votes Only Area 51 has Extra-Terresstrials A(x) = x is Area 51 E(x) = x has Extra-Terresstrials Which of the following is correct? (∀x)(A(x) -> E(x)) (∀x)(E(x) -> A(x)) (∀x)(A(x) <-> E(x)) Mathematical Logic mathematical-logic first-order-logic + – Balaji Jegan asked Sep 27, 2018 • retagged May 7, 2021 by Shiva Sagar Rao Balaji Jegan 517 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Somoshree Datta 5 commented Sep 27, 2018 reply Follow Share Ok I think I got my mistake.. "only area 51 has extra terrestrials" means that if extra terrestrials are present, they can be present only in area 51..but if the area is 51,then that doesn't imply anything about the extra terrestrials.. So for all X, E(X)->A(X) and not vice versa.. So option 2 is correct. 1 votes 1 votes srestha commented Sep 27, 2018 i edited by srestha Sep 27, 2018 reply Follow Share But why for all is used I think there exists is more relevent$\exists x(E(x) \Lambda A(x))$ 0 votes 0 votes Somoshree Datta 5 commented Sep 27, 2018 reply Follow Share @srestha ma'am, Here it is mentioned in the question that only area 51 has extra terrestrials.. So if extra terrestrials is present in any area, then it can be present only in area 51, so for all has to be used. Because if we use there exists, then the predicate will become true even if extra terrestrials is present in an area that isn't area 51 as well as if extra terrestrials is present in the area 51. 0 votes 0 votes Please log in or register to add a comment.
Best answer 0 votes 0 votes This is logically equivalent to saying "If x is an extra terrestrial, it is present in Area 51." Therefore, it can be given as $\forall x (E(x) \rightarrow A(x))$. goxul answered Sep 27, 2018 • selected Sep 27, 2018 by Balaji Jegan goxul comment Share Follow See 1 comment See all 1 1 comment reply himgta commented Feb 11, 2019 reply Follow Share @Balaji Jegan @goxul if E(x) becomes false means x has not extra terrestrial ,then LHS of implication becomes false & overall it becomes true irrespective of RHS! which means if x has not extra terrestrial then x is area 51 is true please clear the doubt! 0 votes 0 votes Please log in or register to add a comment.