Logic Gates - Did I connect them correctly?
There are several errors.  I suggest using WolframAlpha.com to check your logic. In the second problem, for example, for the first gate type in "evaluate (not A) nand (not B)" and you will see that the result is "A or B" instead of the "A and B" that you show.

You will see that "A or B" is the correct answer by applying the first of De Morgan's laws:

not (A and B) == (not A) or (not B)


substituting for your negated inputs:

not ((not A) and (not B)) =&gt; (not (not A)) or (not (not B)) =&gt; A or B


As one of the comments mentioned, you should really start out with non-negated inputs (A, B); you are inconsistent in that regard (you did use a gate to negate D in the first problem).