~(q v ~r)

Start with the letters.
Under both the q and the r, put F, since they are given false.

~(q v ~r)
  F    F 

Next we look for a negation (~) just before a letter, which is ~r
We put the opposite from what the letter is, under the ~.  In this
case since there is an F under the r, we put the opposite T under
the ~

~(q v ~r)
  F   TF

We are done with r, so we erase the F under the r:

~(q v ~r)
  F   T

Inside the parentheses we have v.  Under it we put T if there is at least
one T on one side of the v.  If there are 2 F's one on each side of v, we
put F under v.  So here we put T under the v:

~(q v ~r)
  F T T

Now we are through with the q and the ~, so we erase them.

~(q v ~r)
    T

Only one thing left to take care of, the ~ out front.  So we put the
opposite F, under the ~

~(q v ~r)
F   T

We are through with the v, so we erase it, and we are left with

~(q v ~r)
F 

Answer: B)False
 
Edwin