The line
= p + p' + q + q' should be
= p + p' + q' + q',
which does not reduce to 1.
[EDIT]: See below for a correction.
Hopefully I've uploaded the circuit properly
Using an apostrophe to denote the over-bar (Not), "+" is or, and "." is and, I wrote the initial circuit as:
r = (p'.(p.q).q)'
which I then simplified as follows:
r = p'' + (p.q)' + q'
= p + p' + q + q'
= 1
However, I'm not convinced this is correct. Help please.
Yes. This could also be seen without applying the De Morgan's law (though it's not much of a change). In the original formula, (p'.(p.q).q)', conjunction is associative and p' . p is always false, so p' . p . q . q is false as well. Therefore, its negation is always true.