Artificial intelligent assistant

Why is $\neg (p \land q)$ different than $(\neg p \land \neg q)$? > Why is $\neg (p \land q)$ different than $(\neg p \land \neg q)$? If we let: > p: Blair is a liar > > q: Bush is a liar Then: ¬(p & q) is "Neither Bush nor Blair are liars" which seems to be the same as: (¬p & ¬q) "Bush is not a liar and Blair is not a liar" But the logic tables for them are different. $\neg$(p & q) ($\neg$p & $\neg$q)

"Neither Bush nor Blair are liars" can be written in two equivalent ways:

$$\lnot (p\lor q) \equiv \lnot p \land \lnot q$$

"Not both Bush and Blair are liars"

$$\lnot (p\land q) = \lnot p \lor \lnot q$$

* * *

$\lnot(p\land q)$ means "Not both (p and q)." This means that that either $\lnot p$ or $\lnot$ q.

$\lnot(p \lor q)$ means it's not the case that (either p holds or q holds), i.e. "neither p nor q," This is equivalent, as noted above, to $\lnot$ p

xcX3v84RxoQ-4GxG32940ukFUIEgYdPy 4db80befad437755eef523c9ddacb922