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

2) Statement r is true while s is false.
Which is false?

$
\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}
$

3) Which of the following statements is logically equivalent to $
\neg \left( {p \cup r} \right)
$
?

$
\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}
$

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 $
\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

2. Originally Posted by Tally
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
The integers and the rationals.

3. Originally Posted by Tally
3) Which of the following statements is logically equivalent to $
\neg \left( {p \cup r} \right)
$
?

$
\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}
$

The answer should be A by DeMorgan's Theorem.

4. Originally Posted by Tally
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

2) Statement r is true while s is false.
Which is false?

$
\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}
$

3) Which of the following statements is logically equivalent to $
\neg \left( {p \cup r} \right)
$
?

$
\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}
$

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 $
\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

question (1) has been answered correctly,and also the 1st part of question (3).

Now for question (2) we have that:

only ( T----->F) is false. All other possibilities are true.

According to that none of the cases in question 3 are false unless there is a typo mistake.

For the 2nd part of question 3 we have that:

A $\cap B$={ 2,4,6,8,10} $\cap{ 1,3,5,7,9}$=Φ( the empty set).

And : (A $\cap B$)'= Φ' = U

5. Originally Posted by poutsos.B
question (1) has been answered correctly,and also the 1st part of question (3).

Now for question (2) we have that:

only ( T----->F) is false. All other possibilities are true.

According to that none of the cases in question 3 are false unless there is a typo mistake.

For the 2nd part of question 3 we have that:

A $\cap B$={ 2,4,6,8,10} $\cap{ 1,3,5,7,9}$=Φ( the empty set).

And : (A $\cap B$)'= Φ' = U
r: All men are mortal

s: All dogs are reptiles

does r imply not(s)?

CB

6. Originally Posted by CaptainBlack
r: All men are mortal

s: All dogs are reptiles

does r imply not(s)?

CB

My sentence:

(only ( T----->F) is false. All other possibilities are true)

was referring to the possibilities of T,F In a conditional statement in propositional logic.

The above emanates from the definition of a conditional statement.

Now coming to your case :

Do you want to know :

a) whether the conditional r------>~s is true ,or

b) r logically implies ~s .

Finally the correct statement is;

None of the dogs is a reptile