Talk:Truth table

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Applications[edit]

"This demonstrates the fact that p ⇒ q {\displaystyle p\Rightarrow q} p\Rightarrow q is logically equivalent to ¬ p ∨ q {\displaystyle \lnot p\lor q} {\displaystyle \lnot p\lor q}." Then, logically, isn't one of these functions redundant and therefore completely unnecessary? — Preceding unsigned comment added by 2601:602:780:3926:9526:680D:B40F:658F (talk) 00:10, 25 June 2019 (UTC)[reply]

Dual typo[edit]

It appears Verum ⊤ ought to be the dual of Falsum ⊥ —OK? --Ancheta Wis (talk | contribs) 06:22, 3 July 2020 (UTC)[reply]

p	q		F⁰	NOR¹	↚²	¬p³	↛⁴	¬q⁵	XOR⁶	NAND⁷		AND⁸	XNOR⁹	q¹⁰	→¹¹	p¹²	←¹³	OR¹⁴	T¹⁵
Dual			T¹⁵	NAND⁷	→¹¹	¬p³	←¹³	¬q⁵	XNOR⁹	NOR¹		OR¹⁴	XOR⁶	q¹⁰	↚²	p¹²	→¹¹	AND⁸	F⁰

If you mean De Morgan duality, yes, that is right. You get the De Morgan dual by negating each operand and also the operator: for a constant that is just negating the constant. Glancing over the article didn't reveal what part in particular you are interested in. — Charles Stewart (talk) 06:40, 3 July 2020 (UTC)[reply]

Thank you. I adjusted the typo.

Another question: perhaps Adj deserves a sentence. Might Adj mean 'adjoint' in the Adj row for 'Truth table for all binary logical operators' ? Adjoint is a dab listing. --Ancheta Wis (talk | contribs) 14:56, 4 July 2020 (UTC)[reply]

Implication is associative[edit]

Implies *is* associative. 𝑝→(𝑞→𝑟) should not be read as "p implies that q implies p, but "p implies q which implies r"

The reason why the brackets rule does not work is because of notational peculiarities. Associativity is not about brackets, associativity is about successive applications of an operator, which is different. And the successive applications of the implies operator yield same result independent of the order in which the operations are performed.

Read about https://en.wikipedia.org/wiki/Light%27s_associativity_test — Preceding unsigned comment added by 94.26.72.172 (talk) 17:49, 31 March 2021 (UTC)[reply]

Size of truth table[edit]

Better naming would be ‘number of truth tables’ (for given n; the size of a truth table for n bits is 2^n) — Preceding unsigned comment added by 178.83.38.187 (talk) 15:37, 27 June 2022 (UTC)[reply]