Karnaugh Maps

Hello,

Given the following:
r = x' y' z' + (xy)' + x z' + x' y z'

(a) Draw the Karnaugh map
(b) From the Karnaugh map, find the minimized DNF
(c) Draw the logical circuit corresponding to this minimised DNF.

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Work so far.

(a)What throws me off is the (xy)' part. Using De Morgan's laws, can this be equated to x' + y'. If so, can I write r as:
r = x' y' z' + x' + y' + x z' + x' y z'

Assuming that r can be rewritten as shown above, r = x' y' z' + x' + y' + x z' + x' y z', is this a correct representation of the Karnaugh map:

y' y y y'

x' 1 1 1 1

x 1 1 0 1

z' z' z z

(b) The minimised DNF would then be: x' + y' + z' (from circles in Karnaugh map).

(c) A logic circuit could then be constructed in the following way:
Attachment 27193

I would really appreciate an indication on whether or not I am interpreting this right. Thank you in advance.