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 8.8k 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.