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Does negation only affect variables or does it affect connectives too?

E.g.

Would $\lnot (a \lor b)$ be the same as

This:
$(\lnot a \lor \lnot b)$

Or would it be the same as this:
$(\lnot a \land \lnot b)$

And if it is the second one, then what other connectives would be affected by a negation apart from conjunction ($ \land $) and disjunction ($ \lor $) and how would they be delt with?

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    The *negation* sign applies to **formulae**. – 2017-01-07
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    Formulae are : either *(i)* *atomic*, i.e. (propositional) *variables* : $p, q, \ldots$, or *(ii)* "complex" ones, like $(p \lor q), \lnot p, \ldots$. – 2017-01-07
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    You ask if $\lnot (a \lor b)$ is the same as $(\lnot a \lor \lnot b)$. Have you tried to mak the truth table for these expressions to see if they *are* equal, or anything? – 2017-01-07

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The negation sign applies to formulae.

Formulae are : either (i) atomic, i.e. (propositional) variables: $p,q,\ldots$, or (ii) "complex" ones, like: $(p∨q),¬p,\ldots$

The formula $¬(a∨b)$ is equivalent to : $¬a ∧ ¬b$; see De Morgan's laws.

Similarly: $¬a ∨ ¬b$ is equivalent to $¬(a ∧ b)$.

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    I think that's the truth value of those two end up as equivalent, not the formulae. – 2017-01-08
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    See [Logical equivalence](https://en.wikipedia.org/wiki/Logical_equivalence) : "In logic, statements $p$ and $q$ are *logically equivalent* if they have the same logical content. Two statements are equivalent if they have the same truth value in every model." The truth values are not "equivalent" : they are the same. – 2017-01-08