Thread: truth tables

(p->q)->(p^q)
Write down its truth table

Well P and Q are the only statement variables, so there are four possible inputs:
P true, Q true; P true, Q false; P false, Q true; and P false, Q false.

So you'll need four rows.
The statement is (P->Q) -> (P^Q)
If you let C = P->Q and D = (P^Q) then this is really just C->D, which is elementary.

Code:

             C          D
P    Q     (P->Q)     (P^Q)    C->D
-------------------------------------
T    T       T          T         
T    F       F          F
F    T       T          F   
F    F       T          F

The final column, which is the one continaing the truth possibilities for the given statement, I will leave since it's pretty easy to finish up at this point.