Answer :
Solution :
A logical expression may be defined as those equation or expression which is either viable or inviable.
In the context, translating each statement into a logical expression using the predicates, the quantifiers, and the logical connectives.
Let P(x) be the propositional function "x is perfect"
Let F(x) be the propositional function "x is your friend"
And the domain is all the people
a). No one is perfect
[tex]$\forall \ x \rightharpoondown P(x)$[/tex]
b). Not everyone is perfect.
[tex]$\rightharpoondown \forall \ x\ P(x)$[/tex]
c). All your friends are perfect.
[tex]$\forall \ x (F(x)\rightarrow P(x))$[/tex]
d). At least one of your friends is perfect.
[tex]$\exists \ x \ (F(x) \wedge P(x))$[/tex]
e) Everyone is your friend and is perfect.
[tex]$\forall \ x \ F(x) \wedge \ \forall \ x \ P(x)$[/tex]
f). Not everybody is your friend or someone is not perfect.
[tex]$(\rightharpoondown \ \forall \ x \ F(x) ) \ \wedge (\exists \ x \ \rightharpoondown \ A (x))$[/tex]