Question

Let H(x) be the statement “x is hardworking”, N(x) be the statement “x is naughty” and C(x) be the
statement “ x is clever”, where the domain for x consists of all students. Use quantifications to
express each of the following statements.
a) Some students are clever but naughty.
b) Not all students are clever and hardworking.
c) Some students are clever, hardworking and not naughty.
d) All students are clever, or hardworking or naughty.

Answer 1

Answer a)

$\exist x (C(x)\to N(x))$

Answer b)

$\neg x(C(x) \land H(x))$

Answer c)

$\exist x (C(x)\land H(x)\land\neg N(x))$

Answer d)

$\forall x(C(x)\lor H(x) \lor N(x))$