Answer to Question #247875 in Discrete Mathematics for Fate

Question

Express each of these statements into logical expressions using predicates, quantifiers,

and logical connectives. Let the domain consist of all people. Let S(x) be “x is in your

class,” P(x) be “x is perfect.”

(a) Nobody is perfect. (Use only the universal quantifier.)

(b) Nobody is perfect. (Use only the existential quantifier.)

(c) Nobody in your class is perfect.

(d) Not everybody is perfect.

(e) Someone in your class is perfect.

(f) Not everyone in your class is not perfect.

Answer 1

$S(x)$ be " $x$ is in your class"

$P(x)$ be " $x$ is perfect"

a) $\forall x(\neg P(x))$

b) $\neg \exist x(P(x))$

c) $\neg \exist x(S(x) \wedge P(x))$

d) $\neg \forall x (P(x))$

e) $\exist x (S(x) \wedge P(x))$

f) $\neg \exist x(S(x) \wedge \neg P(x))$