Results 1 to 6 of 6

Math Help - Could someone check the answer please.

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    40

    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?

    <br />
\begin{gathered}<br />
s \to r \hfill \\<br />
\neg s \to r \hfill \\<br />
\neg r \to s \hfill \\<br />
\neg r \to \neg s \hfill \\<br />
r \to \neg s \hfill \\ <br />
\end{gathered} <br />

    Answer C

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

    <br />
\begin{gathered}<br />
\neg p \cap \neg r \hfill \\<br />
p \cup r \hfill \\<br />
\neg (p \cup r) \hfill \\<br />
\neg p \cup \neg r \hfill \\<br />
\neg p \cap r \hfill \\ <br />
\end{gathered} <br />

    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 <br />
\mathop {(A \cap B)}\nolimits^1 <br />
where x denotes that c is a complement of x
    1,2,3,4
    11,12
    0
    1...9
    5...12

    Answer B
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Tally View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Jes
    Jes is offline
    Newbie
    Joined
    Oct 2008
    Posts
    12
    Quote Originally Posted by Tally View Post
    3) Which of the following statements is logically equivalent to <br />
\neg \left( {p \cup r} \right)<br />
?

    <br />
\begin{gathered}<br />
\neg p \cap \neg r \hfill \\<br />
p \cup r \hfill \\<br />
\neg (p \cup r) \hfill \\<br />
\neg p \cup \neg r \hfill \\<br />
\neg p \cap r \hfill \\ <br />
\end{gathered} <br />

    Answer D
    The answer should be A by DeMorgan's Theorem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2008
    Posts
    39
    Quote Originally Posted by Tally View Post
    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?

    <br />
\begin{gathered}<br />
s \to r \hfill \\<br />
\neg s \to r \hfill \\<br />
\neg r \to s \hfill \\<br />
\neg r \to \neg s \hfill \\<br />
r \to \neg s \hfill \\ <br />
\end{gathered} <br />

    Answer C

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

    <br />
\begin{gathered}<br />
\neg p \cap \neg r \hfill \\<br />
p \cup r \hfill \\<br />
\neg (p \cup r) \hfill \\<br />
\neg p \cup \neg r \hfill \\<br />
\neg p \cap r \hfill \\ <br />
\end{gathered} <br />

    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 <br />
\mathop {(A \cap B)}\nolimits^1 <br />
where x denotes that c is a complement of x
    1,2,3,4
    11,12
    0
    1...9
    5...12

    Answer 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
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by poutsos.B View Post
    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
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Oct 2008
    Posts
    39
    Quote Originally Posted by CaptainBlack View Post
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can someone check my answer please?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 25th 2010, 06:49 AM
  2. Please Check my Answer TIA
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: June 19th 2009, 09:15 PM
  3. Please check this answer
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 15th 2008, 10:19 PM
  4. check my answer
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: August 16th 2008, 11:54 AM
  5. z=, check answer please. last one
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 10th 2006, 09:04 PM

Search Tags


/mathhelpforum @mathhelpforum