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Math Help - De morgans methods; simple questions, what do they mean in normal English?

  1. #1
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    Arrow De morgans methods; simple questions, what do they mean in normal English?

    Hi;

    I'm trying to figure out if the following statements are true or not;

    1.
    p v 段 = p -> q

    2. 段 -> 殆 = q -> p

    3. p v (q -> r) = (p v q) -> (p v r)


    Can someone please outline what these lines mean in normal english?

    For example, the start of 1 means; p or not q...

    I don't know what that little arrow actually means...

    Are there any resources online to learn this at basic level?

    Thanks in advance,
    appreciate your time!
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  2. #2
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    Quote Originally Posted by Student122 View Post
    Hi;

    I'm trying to figure out if the following statements are true or not;

    1. p v 段 = p -> q

    2. 段 -> 殆 = q -> p

    3. p v (q -> r) = (p v q) -> (p v r)


    Can someone please outline what these lines mean in normal english?

    For example, the start of 1 means; p or not q...

    I don't know what that little arrow actually means...

    Are there any resources online to learn this at basic level?

    Thanks in advance,
    appreciate your time!
    Hi Student122,

    The little arrow means "implies". p \rightarrow q means p implies q, or simply "if p, then q".

    Sometimes it's written p \implies q

    Do you know what truth table are? Look here: Truth table - Wikipedia, the free encyclopedia

    Code:
     
    p | q |not p | not q | p --> q | not p or q | p or not q
    ---------------------------------------------------------
    T | T | F    |  F    |    T    |       T    |     T
    T | F | F    |  T    |    F    |       F    |     T
    F | T | T    |  F    |    T    |       T    |     F
    F | F | T    |  T    |    T    |       T    |     T
    As you can see from the truth table above, your first implication is false.

    [1] p \vee \neg q \equiv p \rightarrow q is false.

    Their truth values are not the same. Check the truth table.

    But this is true: \neg p \vee q \equiv p \rightarrow q.

    Chech the truth values under their columns.


    Try to set up a truth table to verify the other 2.
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  3. #3
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    Quote Originally Posted by masters View Post
    Hi Student122,

    The little arrow means "implies". p \rightarrow q means p implies q, or simply "if p, then q".

    Sometimes it's written p \implies q

    Do you know what truth table are? Look here: Truth table - Wikipedia, the free encyclopedia

    Code:
     
    p | q |not p | not q | p --> q | not p or q | p or not q
    ---------------------------------------------------------
    T | T | F    |  F    |    T    |       T    |     T
    T | F | F    |  T    |    F    |       F    |     T
    F | T | T    |  F    |    T    |       T    |     F
    F | F | T    |  T    |    T    |       T    |     T
    As you can see from the truth table above, your first implication is false.

    [1] p \vee \neg q \equiv p \rightarrow q is false.

    Their truth values are not the same. Check the truth table.

    But this is true: \neg p \vee q \equiv p \rightarrow q.

    Chech the truth values under their columns.


    Try to set up a truth table to verify the other 2.
    Hi masters,

    Thanks for replying...

    Can I attempt to 'translate' the first question?

    I think it's saying;

    p or not q = p implies q

    So looking at the table, for the first part we look at the last column;

    p | q |not p | not q | p --> q | not p or q | p or not q
    ---------------------------------------------------------
    T | T | F | F | T | T | T
    T | F | F | T | F | F | T
    F | T | T | F | T | T | F
    F | F | T | T | T | T | T

    For the last part of the equation we look at column 5 (in bold & red)

    Correct me if I'm wrong, I probably am (but don't know why lol), but aren't they both True and doesn't that mean that the original sum is true and not false?
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  4. #4
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    Quote Originally Posted by Student122 View Post
    Hi masters,

    Thanks for replying...

    Can I attempt to 'translate' the first question?

    I think it's saying;

    p or not q = p implies q

    So looking at the table, for the first part we look at the last column;

    p | q |not p | not q | p --> q | not p or q | p or not q
    ---------------------------------------------------------
    T | T | F | F | T | T | T
    T | F | F | T | F | F | T
    F | T | T | F | T | T | F
    F | F | T | T | T | T | T

    For the last part of the equation we look at column 5 (in bold & red)

    Correct me if I'm wrong, I probably am (but don't know why lol), but aren't they both True and doesn't that mean that the original sum is true and not false?
    All truth values in the columns must match, not just the first one.

    The red columns don't match.
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  5. #5
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    Quote Originally Posted by masters View Post
    All truth values in the columns must match, not just the first one.

    The red columns don't match.
    Thank you for your reply,

    I understand the whole process now, I went to the learning support office at my uni to, but one thing I don't understand is that not all the 'truth tables' are available or am I mistaken? For example the truth table you have used I couldn't find it on wikipedia!

    I think that I'm meant to write them from scratch..
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  6. #6
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    booltool

    a modern approach to get truth-tables is to use an online-tool like this one. you can enter expressions like "p or not q" directly in the textfield and compare your results with it:

    BoolTool - Onlinerechner fr logische Ausdrcke
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