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Topic: Discrete math! Please help! (Read 3792 times) |
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olenka
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Discrete math! Please help!
« on: Sep 14th, 2008, 7:29pm » |
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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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towr
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Re: Discrete math! Please help!
« Reply #1 on: Sep 15th, 2008, 1:42am » |
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You might want to modify your post to replace the logical operators with something that's legible; because "→" doesn't really tell me much.
This looks a lot like homework, but I'll do 2a) as an example:
step 1, simplify:
red(roses) -> purple(violets)
<=> { rewrite in terms of "not", "and" and "or" operators }
~ red(roses) or purple(violets)
step 2, the negation of the statement:
~[~ red(roses) or purple(violets)]
<=> { DeMorgan }
~~ red(roses) and ~purple(violets)
<=> { simplify, in this case removing double negations }
red(roses) and ~purple(violets)
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