Construct a truth table for (~p ^ q) ↔ p

Question

Construct a truth table for (~p ^  q) ↔ p

anonymous · Answer

p        q     p    ~p     (~p^q)--> p
t         t      t      f          f
t         f      t      f          f
f         t      f      t          f
f         f      f      t          t

jim_thompson5910 · Answer

btw, you only have to have one p column and it might help to construct the ~p ^ q column

anonymous · Answer

so thats why i got messed up on the final column.. cuz i  put 2 p's

jim_thompson5910 · Answer

yeah that might've been it, but it also might have been you were missing the ~p ^ q column

anonymous · Answer

Double implication...

jim_thompson5910 · Answer

oh my bad

jim_thompson5910 · Answer

thought it was a normal implication, I'll fix it

jim_thompson5910 · Answer

here's the correction

p      q        ~p        ~p ^ q          (~p ^ q) <--> p
--------------------------------------------------------
T      T         F          F                  F
T      F         F          F                  F
F      T         T          T                  F
F      F         T          F                  T

jim_thompson5910 · Answer

notes: p <--> q is true if the truth values of p and q are the same (ie they are both true or both false)