Every integer is a rational number -> false -- correct?
Let r = true; s = true. Is this statement true or false? $$\lnot [r \lor (\lnot s \lor r)];\quad$$ -> true -- correct?
Let p = true; r = false; q = false. Is the following statement true or false? $$\lnot [\lnot q \lor(p \lor \lnot r)$$ -> false -- correct?
You didn't strike out, but only one of your answers is correct:
Note that any integer $n$ can be expressed as the fraction: $\dfrac n1$. (In all fairness, the answer depends on how the rational numbers are defined. If we define the integers as a proper subset of the rationals, as suggested by my note, then your answer should be true.)
This is in fact false. $$\lnot[T \lor (F \lor T)] \equiv \lnot [T \lor T] \equiv \lnot [T] = F$$
Correct: "false" is the correct answer. $$\lnot [\lnot q \lor(p \lor \lnot r)] \equiv \lnot[\lnot F \lor T \lor\lnot F] \equiv \lnot[T] \equiv F$$