37 votes 37 votes The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$ Mathematical Logic gatecse-2014-set3 mathematical-logic easy first-order-logic + – go_editor asked Sep 28, 2014 • edited Jun 8, 2018 by kenzou go_editor 7.9k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments `JEET commented Dec 18, 2019 reply Follow Share Can I write logic for "All rainy days are cold." and then do the negation. Will that be correct? 0 votes 0 votes Verma Ashish commented Dec 18, 2019 reply Follow Share Yes. That will be correct. 3 votes 3 votes `JEET commented Dec 18, 2019 reply Follow Share Thanks! 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes "Not all Rainy days are Cold" are also rewrite “There exists at least one Rainy day are not Cold” Lakshman Bhaiya answered Feb 19, 2018 Lakshman Bhaiya comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes "not all Rainy days are Cold" ~∀d (Rainy(d) —> Cold(d)) ~∀d (~Rainy(d) + Cold(d)) ∃d (Rainy(d) ^ ~ Cold(d)) Some rainy days are not cold. i hope my answer helps u a lot. akshay_123 answered Sep 1, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.
–1 votes –1 votes Not all rainy days are cold which is $\neg(\forall d(\text{Rainy}(d)\rightarrow \text{Cold}(d) ))$ $\neg(\forall d(\neg\text{Rainy}(d) \lor \text{Cold}(d) ))$ $(\exists \neg d(\neg\text{Rainy}(d) \lor \text{Cold}(d) ))$ $(\exists d(\text{Rainy}(d) \land \neg\text{Cold}(d) ))$ Option $D$ Rishi yadav answered Aug 21, 2017 • edited Apr 20, 2019 by Rishi yadav Rishi yadav comment Share Follow See 1 comment See all 1 1 comment reply air1ankit commented Oct 1, 2017 reply Follow Share we get to conclusion 1.some rainy day are cold or 2.some rainy day are not cold so according to option d we get sme rainy day are not cold .. so may be it is correct method . if i am in correct then please correct me 1 votes 1 votes Please log in or register to add a comment.