33 votes 33 votes What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” $\exists x (\text{real}(x) \lor \text{rational}(x))$ $\forall x (\text{real}(x) \to \text{rational}(x))$ $\exists x (\text{real}(x) \wedge \text{rational}(x))$ $\exists x (\text{rational}(x) \to \text{real}(x))$ Mathematical Logic gatecse-2012 mathematical-logic easy first-order-logic + – gatecse asked Aug 5, 2014 edited Jun 20, 2017 by Silpa gatecse 8.5k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Mohitdas commented Oct 23, 2021 reply Follow Share just a Hint Use ^ for there exist(∃) 0 votes 0 votes Mohitdas commented Oct 23, 2021 reply Follow Share for ALL ∀x(rational(x)→real(x)) 0 votes 0 votes Please log in or register to add a comment.
Best answer 49 votes 49 votes Meaning of each choices: There exists a number which is either real or rational If a number is real it is rational There exists a number which is real and rational There exists a number such that if it is rational, it is real So, (C) is the answer. Arjun answered Aug 21, 2014 edited Jun 8, 2018 by kenzou Arjun comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Mayank0343 commented Dec 3, 2019 reply Follow Share Hi @Ayush Upadhyaya sir, I get confused when to translate a statement as AND (^) and when to use implication (-->) . eg. None of my friends are perfect... here should i consider Friends ^ Perfect or Friends-->Perfect For statement : Good mobile phones are not cheap. (from gate 2014) i used implication and that leads to the right answer. Similarly Not all that glitters is gold(2014) also implication gives the correct result Any tips or any source to refer pls 0 votes 0 votes fahad1247 commented Oct 5, 2020 reply Follow Share suppose the number is complex so real(x) is false but real(x) → rational(x) will be true but rational numbers are not complex 0 votes 0 votes himanshud2611 commented Jan 20 reply Follow Share @Gate Fever, option d says, If there exists a rational number, it is real. Which isn’t same as statement asked. 0 votes 0 votes Please log in or register to add a comment.
6 votes 6 votes “ There exists a number which is real and rational” and this is equal to “Some real number are rational number.” Lakshman Bhaiya answered Feb 19, 2018 edited Feb 19, 2018 by Lakshman Bhaiya Lakshman Bhaiya comment Share Follow See all 4 Comments See all 4 4 Comments reply Nandkishor3939 commented Sep 28, 2019 reply Follow Share Rational numbers are always real 8 votes 8 votes rajankakaniya commented Jun 25, 2021 reply Follow Share If possible, can you please draw the ven diagrams for other options given in question ? It might be helpful. @LakshmanPatelRJIT 0 votes 0 votes Lakshman Bhaiya commented Jun 25, 2021 reply Follow Share You can try it out. 1 votes 1 votes rajankakaniya commented Jun 27, 2021 reply Follow Share Please, check and correct if wrong. https://gateoverflow.in/?qa=blob&qa_blobid=4820487837657352897 And which tool you used for image ? Don’t know why my image is rotated. :) 0 votes 0 votes Please log in or register to add a comment.
4 votes 4 votes (C) is the answer. Translation of (C):" There exists a number which is real and rational " and this is eqt to “Some real numbers are rational”. Warrior answered Jul 18, 2017 Warrior comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes short trick Use ^ for “there exist(∃)” use → for “for ALL” according to this option c is correct akshay_123 answered Sep 23, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.