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        riddles >> medium >> Discrete math! Please help!
        
(Message started by: olenka on Sep 14^th, 2008, 7:29pm)

Title: Discrete math! Please help!
Post by olenka on Sep 14^th, 2008, 7:29pm

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!!!! ???

Title: Re: Discrete math! Please help!
Post by towr on Sep 15^th, 2008, 1:42am

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)