Negation bar meaning?

Question

I know that the horizontal bar on top means it's a negation. But I've never encountered one over more than one term like this one:

$\overline{\bar{x} + \bar{y}x}(y + \overline{xy})$

Is that equivalent to:

($\neg{(\bar{x} + \bar{y}x))}(y + \overline{xy})$ (the 2 first terms are negated then they are multiplied by the two last terms)

or

$\neg{\bar{x}} + (\neg{\bar{y}x)}(y + \overline{xy})$ (the first two terms are negated, but only the second term is multiplied by the two last terms)

or just.. something else?

Thanks!

Answer 1

Your first intuition was correct, it is equivalent to

$$ \left(\neg\left(\overline{x}+\overline{y}x\right)\right)\left(y+\overline{xy}\right)=\neg\left(\neg x+\left(\neg y\right)x\right)\left(y+\neg\left(xy\right)\right) $$

Answer 2

The first equivalence you have given was the correct one.

You can use the De-Morgan's Law to simplify it.