These are indeed equivalent, and this identity is one of DeMorgan's laws.
The 6th column is the negation of the 5th column. For example, the first row says
not <em>p</em> or <em>q</em>
is true (T), so the negation would be false (F). The 5th column reads {T, F, T, T}, so the next column should be {F, T, F, F}.
Then in the 7th/last column, you are checking the truth value of the statement
<em>p</em> and not <em>q</em>
For example, in the first row, both <em>p</em> and <em>q</em> are true (T). This means (not <em>q</em>) is false, so (<em>p</em> and not <em>q</em>) is false (F). The last column should end up reading {F, T, F, F}, same as the previous column.
