Question

Symbolize the following by using qualifiers, predicates and logical connectives.

1. All rational numbers are real numbers.
2. some rational numbers are integers.
3. some even numbers are multiplied of two four and five.
4. some triangles are scalene.
5. every integer is multiple of 10 if and only if it is a mulple of 5 and 2.

Answer 1

Consider

$Q(x)$ set of rational numbers

$R(x)$ set of real numbers

$E(x)$ det of even numbers

$S(T)$ set of triangles

All rational numbers are real numbers.

$\forall xQ\left( x \right) \to R\left( x \right)$

some rational numbers are integers.

$\exists x\left( {Q\left( x \right) \wedge Z\left( x \right)} \right)$

1. some even numbers are multiplied by two four and five.

$\exists x\left( {E\left( x \right) \wedge {M_2}\left( x \right) \wedge {M_5}\left( x \right)} \right)$

some triangles are scalene.

\exists TS\left( T \right)\

every integer is a multiple of 10 if and only if it is a multiple of 5 and 2.