Answer
a. Kwame will not take a job in industry and Kwame will not go to graduate school.
b. Yoshiko does not know Java or Yoshiko does not know calculus.
c. James is not young or James is not strong.
d. Rita will not move to Oregon and Rita will not move to Washington.
Work Step by Step
$\neg(p\wedge q) \equiv \neg p\vee\neg q$
$\neg(p\vee q) \equiv \neg p\wedge\neg q$
---
$a.$
NOT [ (Kwame will take a job in industry ) OR (Kwame will go to graduate school)]
is equivalent to
(Kwame will not take a job in industry ) and (Kwame will not go to graduate school)
$b.$
NOT [ (Yoshiko knows Java) AND (Yoshiko knows calculus)]
is equivalent to
(Yoshiko does not know Java) or (Yoshiko does not know calculus)
$c.$
NOT [ (James is young ) AND (James is strong)]
is equivalent to
(James is not young) or (James is not strong)
$d.$
NOT [ (Rita will move to Oregon ) OR (Rita will move to Washington)]
is equivalent to
(Rita will not move to Oregon ) and (Rita will not move to Washington)
