40 votes 40 votes Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ is precious $\forall x(P(x) \implies (G(x) \wedge S(x)))$ $\forall x((G(x) \wedge S(x)) \implies P(x))$ $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$ Mathematical Logic gatecse-2009 mathematical-logic easy first-order-logic + – gatecse asked Sep 15, 2014 edited Jun 6, 2018 by kenzou gatecse 8.3k views answer comment Share Follow See all 10 Comments See all 10 10 Comments reply Show 7 previous comments pavan singh commented Jun 7, 2023 reply Follow Share @Deepak PooniaAssume, p: gold ornament is precious. q: silver ornament is precious. In case of "$\vee$" p & q both can be True, i.e. we can say that p & q both are precious. But in case of "$\oplus$" p & q both can't be True. So, we can't say that p & q both are precious. That's why we can't use Exclusive-or becoz in question given statement is "Gold & Silver ornaments are precious. "Sir, am i correct???? 0 votes 0 votes Deepak Poonia commented Jun 7, 2023 i edited by Deepak Poonia Jun 7, 2023 reply Follow Share Please read & analyze what I have written in the previous comments. You are asking your pre-determined doubts without analyzing what I have written. 1. Watch This Lecture till time 00:33:20.2. After watching the above lecture, read This Comment.Assume the domain contains boys and girls. In the domain, an element is either a boy or girl but not both. Now, the statement “everyone is either a boy or a girl” can be expressed as: $\forall x (B(x) \oplus G(x)) $ Or $ \forall x (B(x) \vee G(x))$.. Both are correct. Also read This Comment.Similar question: GATE CSE 2006 | Question: 26 2 votes 2 votes pavan singh commented Jun 7, 2023 reply Follow Share @Deepak Poonia Thanks Sir..... Actually I didn't know this concept. Thanks again..... 1 votes 1 votes Please log in or register to add a comment.
Best answer 56 votes 56 votes The statement could be translated as, if $x$ is either Gold or Silver, then it would be precious. Rather than, If $x$ is both Gold and Silver, as an item cannot both Gold and silver at the same time. Hence Ans is (D). sonapraneeth_a answered Jan 20, 2015 edited Feb 17, 2021 by soujanyareddy13 sonapraneeth_a comment Share Follow See all 3 Comments See all 3 3 Comments reply Rohan Mundhey commented Oct 11, 2016 reply Follow Share well , if we think about it an item can be both gold and silver at the same time BUT here in this context an item cant be gold and silver at same time because here gold & silver items are disjoint sets ... it's something we have to understand from the question 22 votes 22 votes Sandeep Suri commented Jan 14, 2017 reply Follow Share Yes "and" word is confusiing and leading to wrong answer. Ornament can not be both Gold and Silver at same time. 9 votes 9 votes Verma Ashish commented Jan 11, 2019 reply Follow Share These logic are more confusing. Sometimes propositions doesn't convey any real meaning if we try to solve them according to simple english sentence then we might do it wrong. But here we have to use intuition.. / 3 votes 3 votes Please log in or register to add a comment.
9 votes 9 votes "Gold and silver ornaments are precious" For all x, x can be either Gold or Silver ornament then the x is precious. Lakshman Bhaiya answered Feb 19, 2018 Lakshman Bhaiya comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Option D this is just Same as lion and tiger question https://gateoverflow.in/989/gate2006-26 Rishi yadav answered Aug 22, 2017 Rishi yadav comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes This statement can be expressed as => For all X, x can be either gold or silver then the ornament X is precious => For all X, (G(X) v S(x)) => P(X). Regina Phalange answered Apr 15, 2017 Regina Phalange comment Share Follow See all 0 reply Please log in or register to add a comment.