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Math Help - logic statement

  1. #1
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    Exclamation logic statement

    1. For [ ( p → q ) ʌ q ] → p make up the statement for p and one for q, then write a statement of this form in words to illustrate that this statement form is sometimes false.

    2. The negation of statement form like pʌq can be written "not(pʌq)" or " it is false that pʌq" but these are considered trivial negations. A non trivial negation will change the form of the statement. For example using DeMorgans Law the negation of (pʌq) can be written (not p ᴠ not q). Using some of the logical equivalences on the tautology sheet write a non trivial negation of each of the following statements:

    a) If roses are red then violets are purple.

    b) Triangle ABC is isosceles or it is scalene

    C) A figure is a parallelogram if and only if it is a rectangle. Please Help
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  2. #2
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    Quote Originally Posted by olenka View Post
    1. For [ ( p → q ) ʌ q ] → p make up the statement for p and one for q, then write a statement of this form in words to illustrate that this statement form is sometimes false.

    2. The negation of statement form like pʌq can be written "not(pʌq)" or " it is false that pʌq" but these are considered trivial negations. A non trivial negation will change the form of the statement. For example using DeMorgans Law the negation of (pʌq) can be written (not p ᴠ not q). Using some of the logical equivalences on the tautology sheet write a non trivial negation of each of the following statements:

    a) If roses are red then violets are purple.

    b) Triangle ABC is isosceles or it is scalene

    C) A figure is a parallelogram if and only if it is a rectangle. Please Help
    Let .....p= i go to London and q= i buy a car ,hence :



    I say If i go to London i will buy a car (p---->q) and so happens that i bought a car .........[(p---->q) ^ q] .Can we conclude then that i went to London???..................[(p---->q) ^ q]------>q???



    .....................................NO................................................ .......

    I COULD have bought the car in Paris

    On the other hand if i say that:

    if i go to London i will visit the Bloody Tower and it so happens that i did visit the Bloody Tower ,what can be said now ??

    .............did or did not go to London??.......................................... ......


    NOW for question 2 we have:

    a) Let p=roses are red and q= violets are purple .The negation of p---->q (= if roses are red then violets are purple) is ~(p---->q), which is equivalent ~( ~pvq) which is equivalent to p^ ~q (=roses are red and the violets are not red).

    So we say that,if it is not true that : if roses are red then violets are purple,then :roses are red and violets are not purple


    b) the negation of "b" is that:

    ABC is not isosceles and ABC is not scalene

    For question "a" p--->q is equivalent to ~pvq and now the negation of that ~(~pvq) through De Morgan law is equivalent ...............p^~q
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  3. #3
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    Question

    Thank you so much ...but what about problem 2c?
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  4. #4
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    I AM sorry for the moment i got lost.


    2c is a biconditional.

    let p= S is para//gram and q= S is square then we have :

    ...................................p<------>q............................................1

    and the negation of that is:

    ................................((~p& q) v(p& ~q)).......................................2

    NOTE IN the above instead of "a figure" i used S.

    Also .........................p<------->q is equivalent to ........[(p----->q)^(q------->p)]..................3

    Now by negating 3 try to arrive to ..................................2
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  5. #5
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    Thumbs up

    Thank you so much U R The BEST !!!!!
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