## Task 4 - 221214

Determine all real numbers $x$ that have the property that of the following statements (A) to (F), four are true and two are false!

(A) $x$ is a positive rational number.

(B) $x$ is a natural number, or $x$ can be represented in the form $x=\frac{1}{g}$ with an integer $g \neq 0$.

(C) $x^{2}$ is an integer, but $x$ itself is not an integer.

(D) $7 < x^{2} < 9$.

(E) $x$ is a positive real number, but not a natural number.

(F) If $x$ is rational, then $x$ is an integer.

Hint: A statement of the form "If $p$, then $q$ " is true if and only if the statement "(not $p$) or $q$ " is true. A statement of the form " $u$ or $v$ " is true if and only if at least one of the two sub-statements $u$ and $v$ is true.