The Gateway to Computer Science Excellence
+1 vote
1.2k views
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.
in Mathematical Logic by | 1.2k views

4 Answers

+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))

by
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

by
+1

part d) can be thought in this way "there exists a friend of yours that is perfect". In logic, it will be: ∃x(F(x) ^ P(x))

0
it tells that there is only one friend but there may be 2 3 4 5 6 friends and so on which are perfect so how to include that in above logic...??
0

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
k :)
0

is there any answer for this to write in logic"ALL FRIENDS ARE PERFECT - NO FRIEND IS PERFECT"

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) $\exists y \forall x F(x) \wedge P(y)$
by
0
Why y and x in d?
0
For all the friends, there is someone who is perfect.
0
But that's not the question rt? The perfect person must be one among the friends.
0
My mistake, Thank you.
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))
by

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
52,375 questions
60,610 answers
202,044 comments
95,428 users