Could someone check the answer please.

I just took a test and was wondering if someone could check a few of my answer. If they are wrong could you give me a brief explanation. My answers are after the question. Thanks

1. Which of the following is a countably infinite set.

a) Real Numbers

b) Integers

c) Rational numbers

d) Irrational numbers

e) Complex number

Answer a

2) Statement r is true while s is false.

Which is false?

$\displaystyle

\begin{gathered}

s \to r \hfill \\

\neg s \to r \hfill \\

\neg r \to s \hfill \\

\neg r \to \neg s \hfill \\

r \to \neg s \hfill \\

\end{gathered}

$

Answer C

3) Which of the following statements is logically equivalent to $\displaystyle

\neg \left( {p \cup r} \right)

$?

$\displaystyle

\begin{gathered}

\neg p \cap \neg r \hfill \\

p \cup r \hfill \\

\neg (p \cup r) \hfill \\

\neg p \cup \neg r \hfill \\

\neg p \cap r \hfill \\

\end{gathered}

$

Answer D

U 1,2,3...12 A=2,4,6,8,10 B=1,3,5,7,9 C=1,2,3,4

Which of the following set is specified by $\displaystyle

\mathop {(A \cap B)}\nolimits^1

$ where x denotes that c is a complement of x

1,2,3,4

11,12

0

1...9

5...12

Answer B