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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.

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• 3 weeks later...

Here I am, the first (and obviously the best) one to help, no edits (which means I won't edit it if there is an error, which gladly there isn't any)

this guy already did 2a for ya, he's most likely to be correct, but since I'm not the one that solved it I can't make promises. I'll solve the rest. Yeah that's right, all of them. Why? Cos that's what I do, I solve problems (and brag about doing so).

But don't be so happy just yet, because I'm also a mathematical minimalist (besides being a conversationalist, apparently). My solutions are neat and I won't explain them in words. Try to understand them yourself. The capital letter V denotes disjunction.

start of solution

2b) ~(iVs) <=> ~iʌ~s

2c) ~(p⊙r) <=> ~[(pʌr)V(~pʌ~r)] <=> ~(pʌr) ʌ ~(~pʌ~r)

1)

p: I am ugly. This is a false statement.

q: My girlfriend is pretty. This is a true statement.

[(p→q)ʌq]→p <=> [(0→1)ʌ1]→0 <=> [1ʌ1]→0 <=> 0

end of solution

If you respect me, you should only go to Mathworld for more info.

Hopefully your homework isn't due yet, is it? Feel free to notify me when you have any future discrete problems.

I'm only being such a nice guy to impress my on-and-off girlfriend. She is always impressed when I solve something that has exclusive disjunction in it (this thread came close). I wonder why. I hope I'm not acting too cheesy, am I? This is actually the only unsolved problem on the Internet that I can solve.

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