Question 483286
you have three variables.
they are p, q, and r.
your compound statement is p ^ (q v ~r)
in english that would be:
p AND (q OR (not r))
here's your truth table:
<pre>
           p   q   r   ~r   (q v ~r)   p ^ (q v ~r)
           -   -   -   --   --------   ------------
           T   T   T    F       T          T *****
           T   T   F    T       T          T *****
           T   F   T    F       F          F
           T   F   F    T       T          T *****
           F   T   T    F       T          F
           F   T   F    T       T          F
           F   F   T    F       F          F
           F   F   F    T       T          F
</pre>
from this table, you can see that:
if p is true and (q or ~r) is true, then p ^ (q v ~r) is true.
in all other cases, p ^ (q v ~r) is false.


note that only one of q and ~r has to be true in order for the compound statement of (q v ~r) to be true.
if p is true, then the OR statement is true.
if ~q is true, then the OR statement is true.
The OR statement is only false if both p and q are false.