1 votes 1 votes Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. a) No one is perfect. b) Not everyone is perfect. c) All your friends are perfect. d) At least one of your friends is perfect. focus _GATE asked Jul 8, 2015 focus _GATE 12.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes a) No one is perfect. == Not ( one is perfect) = ~ (∃x(px))= ∀x ~p(x)= Every one is imperfect.b) Not everyone is perfect.== Not (everyone is perfect.)= ~( ∀x(px))=∃x ~p(x)= Atleast one is imperfect.c) All your friends are perfect. == if there is a person who is your friend then he is perfect== ∀x( F(x)→P(x))d) At least one of your friends is perfect. == There is a person who is your friend who is perfect. ∃x (F(x)∧P(x)) Prashant. answered Nov 27, 2015 Prashant. comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes plz correct me if wrong!! P(x) : perfect F(x) :friends (a)∽∃x(P(x)) (b)∽∀x(P(x)) (c)∀x(F(x)------>P(x)) (d) i am thinking in this way ALL FRIENDS ARE PERFECT - NO FRIEND IS PERFECT how to write above sentence...?? in logic focus _GATE answered Jul 8, 2015 focus _GATE comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments Vivek sharma commented Jul 8, 2015 reply Follow Share nopes. ∃x(P(x)) can also be read as: 1)there is atleast one x such that P(x) is true 2) for some x, P(x) is true. 0 votes 0 votes focus _GATE commented Jul 8, 2015 reply Follow Share k :) 0 votes 0 votes focus _GATE commented Jul 8, 2015 reply Follow Share is there any answer for this to write in logic"ALL FRIENDS ARE PERFECT - NO FRIEND IS PERFECT" 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Equivalent answers, $P(x):$ X is Perfect $F(x):$ X is a friend of mine (a) $\forall x \neg P(x)$ (b) $\exists x \neg P(x)$ (c) $\forall x, F(x) \rightarrow P(x)$ (d) $\exists y \forall x F(x) \wedge P(y)$ Salman answered Sep 2, 2015 Salman comment Share Follow See all 4 Comments See all 4 4 Comments reply Arjun commented Sep 2, 2015 reply Follow Share Why y and x in d? 0 votes 0 votes Salman commented Sep 2, 2015 reply Follow Share For all the friends, there is someone who is perfect. 0 votes 0 votes Arjun commented Sep 2, 2015 reply Follow Share But that's not the question rt? The perfect person must be one among the friends. 0 votes 0 votes Salman commented Sep 2, 2015 reply Follow Share My mistake, Thank you. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes P(x) : perfect F(x) :friend a) ∽∃x(P(x)) B) ∽∀x(P(x)) C) ∀x(F(x)->P(x)) D) ∃x(Friend(x) ^ Perfect(x)) Akash Kanase answered Nov 27, 2015 Akash Kanase comment Share Follow See all 0 reply Please log in or register to add a comment.