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