• Oct 22nd 2008, 06:41 PM
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

• Oct 22nd 2008, 07:12 PM
ThePerfectHacker
Quote:

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.
• Oct 23rd 2008, 12:26 AM
Jes
Quote:

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.
• Oct 23rd 2008, 04:50 AM
poutsos.B
Quote:

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
• Oct 23rd 2008, 05:30 AM
CaptainBlack
Quote:

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
• Oct 23rd 2008, 11:06 AM
poutsos.B
Quote:

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