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))

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+1 vote

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.

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.

+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))

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

+1

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...??

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