Answer to Question #222813 in Discrete Mathematics for sonia Akter

Question

Express each of these statment using quantifires :
a) every student in this classes has taken exactly two mathematics classes at this school.
b) someone has visited every country in the world except Libya

Answer 1

b.) Let $B(x,y)$ represent that $x$ has visited a country $y$.

So, the above statement is quantified as;

$\exists x \forall y, \neg B(x,y) \leftrightarrow y= Libya.$

a.) Let $M(x)$ represent $x$ is a math course at this school. So the statement above is quantified as;

$\forall x (S(x) \to \exists y \exists z (y \neq z \wedge \forall w((w = y \vee w=z) \leftrightarrow (M(w) \wedge T(x,w))))$ .