26 votes 26 votes For a person $p$, let $w(p)$, $A(p, y)$, $L(p)$ and $J(p)$ denote that $p$ is a woman, $p$ admires $y$, $p$ is a lawyer and $p$ is a judge respectively. Which of the following is the correct translation in first order logic of the sentence: "All woman who are lawyers admire some judge"? $\forall x: \left[\left(w\left(x\right)\Lambda L \left(x\right)\right)\Rightarrow \left(\exists y:\left(J \left(y\right)\Lambda w\left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$ $\forall x: \left[\left(w\left(x\right)\Rightarrow L \left(x\right)\right)\Rightarrow \left(\exists y:\left(J \left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$ $\forall x \forall y: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right]$ $\exists y \forall x: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right]$ $\forall x: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(\exists y: \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$ Mathematical Logic tifr2012 mathematical-logic first-order-logic + – makhdoom ghaya asked Oct 30, 2015 edited Aug 17, 2020 by soujanyareddy13 makhdoom ghaya 2.1k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 41 votes 41 votes Just translating to English: Every women who is a lawyer admires some women judge. If a person being women implies she is a lawyer then she admires some judge. OR If a person is not women or is a lawyer he/she admires some judge. Every women who is a lawyer admires every judge. There is some judge who is admired by every women lawyer. Every women lawyer admire some judge. So, option (e) is the answer. Arjun answered Nov 19, 2015 edited Jun 8, 2018 by kenzou Arjun comment Share Follow See 1 comment See all 1 1 comment reply talha hashim commented May 25, 2018 reply Follow Share nice explanation @Arjun sir 0 votes 0 votes Please log in or register to add a comment.
3 votes 3 votes It will be (e). srestha answered Oct 31, 2015 edited Jun 8, 2018 by kenzou srestha comment Share Follow See all 4 Comments See all 4 4 Comments reply Tendua commented Nov 17, 2015 reply Follow Share i think e will be right still why d is wrong. both conclude the same thing. is this a multiple answer question ? 0 votes 0 votes sonu commented Nov 19, 2015 reply Follow Share d is wrong becz it is ∃y∀x. It means All woman will admire same judge. But it should be other way. ∀X∃y. Then D will be true. 2 votes 2 votes Prashant. commented Nov 19, 2015 reply Follow Share ∃y∀x and ∀x∃y are two differnt things. ∃y∀x thier exist some y for all x. ∀x∃y for all x thier exist a y. 11 votes 11 votes Tendua commented Nov 19, 2015 reply Follow Share i got that one. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes (e) is the correct translation. ∀x:[(w(x)ΛL(x))⇒(∃y:(J(y)ΛA(x,y)))] :"For every person x, if x is woman AND lawyer then she admires some judge" which is equivalent to say "Every women lawyer admire some judge" . So, Ans is (e). Warrior answered Jul 18, 2017 Warrior comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Caption Prashant. answered Nov 19, 2015 Prashant. comment Share Follow See all 0 reply Please log in or register to add a comment.