Willem F Esterhuyse Posted January 16, 2023 Share Posted January 16, 2023 I saw in a writing: ~p -> p = false. This can't be true since 0 -> 1 = 1, so ~p -> p = p! Link to comment Share on other sites More sharing options...
Genady Posted January 16, 2023 Share Posted January 16, 2023 It can be true since 1 -> 0 = 0. Link to comment Share on other sites More sharing options...
Lorentz Jr Posted January 16, 2023 Share Posted January 16, 2023 (edited) 3 hours ago, Willem F Esterhuyse said: I saw in a writing: ~p -> p = false. This can't be true since 0 -> 1 = 1, so ~p -> p = p! p is a proposition, not a number. If p is "Love is blind", then ~p -> p would mean "If love is not blind, then love is blind." That can't be true, because either love is blind or it's not blind. EDIT: Okay, this isn't technically a contradiction. It's considered true if p is true, and of course it's false if p is false. "~p ↔ p" would be a contradiction. Edited January 16, 2023 by Lorentz Jr Link to comment Share on other sites More sharing options...
studiot Posted January 16, 2023 Share Posted January 16, 2023 You have to be very careful with negating a compound proposition or statement. For example the negation of "love is blind" could be "something other than love is blind" eg "A worm is blind" . In this case not p is true. Link to comment Share on other sites More sharing options...
Genady Posted January 16, 2023 Share Posted January 16, 2023 2 hours ago, Lorentz Jr said: p is a proposition, not a number. I assume that 0 and 1 in OP don't stay for arithmetic numbers, but rather represent logical values, which by usual convention are: 0 for FALSE and 1 for TRUE. Link to comment Share on other sites More sharing options...
Lorentz Jr Posted January 16, 2023 Share Posted January 16, 2023 6 minutes ago, Genady said: I assume that 0 and 1 in OP don't stay for arithmetic numbers, but rather represent logical values, which by usual convention are: 0 for FALSE and 1 for TRUE. I see. I guess I should have figured that out. Maybe time for some coffee. Link to comment Share on other sites More sharing options...
swansont Posted January 16, 2023 Share Posted January 16, 2023 5 hours ago, Willem F Esterhuyse said: since 0 -> 1 = 1 Can you demonstrate that this is true? Link to comment Share on other sites More sharing options...
Willem F Esterhuyse Posted January 17, 2023 Author Share Posted January 17, 2023 18 hours ago, swansont said: Can you demonstrate that this is true? No, you learn it from the truth table for "therefore". There is a reason for it though, more of a convention. 1 Link to comment Share on other sites More sharing options...
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