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wu :: forums    riddles    medium (Moderators: Eigenray, william wu, SMQ, Grimbal, Icarus, towr, ThudnBlunder)    Is p->q->q a tautology? « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Is p->q->q a tautology?  (Read 2849 times) techno Newbie     Posts: 4 Is p->q->q a tautology?   « on: Sep 26th, 2012, 4:36pm » Quote Modify note that there are no parenthesis. Thanks for the help   IP Logged Noke Lieu Uberpuzzler pen... paper... let's go! (and bit of plastic)     Gender: Posts: 1884 Re: Is p->q->q a tautology?   p_to_q.png « Reply #1 on: Sep 26th, 2012, 7:07pm » Quote Modify Depends on what you mean...   Not in this case. IP Logged a shade of wit and the art of farce. techno Newbie     Posts: 4 Re: Is p->q->q a tautology?   « Reply #2 on: Sep 26th, 2012, 9:03pm » Quote Modify I think that's exactly what I meant. Thanks. But how would you solve it? What I did was this.   p->q->q   -p || (q->q)   -p || (-q||q)   -p || (T)   T.   Can you please explain me where I did something wrong? thanks for the help.   Or is it like this? I think this makes more sense but still.     p->q->q   (-p || q)->q   -(-p || q) || q   (p && q) || q   (p || q) && (q || q)   q && (p || q)   Thanks for replying so quickly.   IP Logged techno Newbie     Posts: 4 Re: Is p->q->q a tautology?   « Reply #3 on: Sep 26th, 2012, 9:06pm » Quote Modify Actually I was wrong on the last thing I did.   It's     (p && -q) || q   (q || p) && (-q || q)   ( q || p ) && T   ( q || p ) IP Logged peoplepower Junior Member     Posts: 63 Re: Is p->q->q a tautology?   « Reply #4 on: Sep 27th, 2012, 5:18am » Quote Modify A self-implication is a tautology, so implying a self-implication is still a tautology. I have personally seen implication as a right-associative operation exclusively, where we have in general p->(q->r) <=> ~pV(~qVr) <=> ~(p&q)Vr <=> (p&q)->r. IP Logged techno Newbie     Posts: 4 Re: Is p->q->q a tautology?   « Reply #5 on: Sep 27th, 2012, 8:56am » Quote Modify That was my main concern. So it is a right associative operation. Thanks for the help appreciate it   IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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