Truth tables and implications

1. Sep 8, 2011

Easy_as_Pi

1. The problem statement, all variables and given/known data
For statements P, Q, and R, use a truth table to show that each of the following pairs of statements are logically equivalent.
a) (P^Q) <=> P and P=>Q
b) P=>(Q v R) and (~Q)=>(~P v R)

3. The attempt at a solution
See attached truth tables.
Basically, I have no idea how to correlate P and QvR in the table. If P is false or QvR is true, then the implication is true; I know that. I know P can only have 2 values, true or false, but QvR is only false under one condition. So, is P true or false in that slot? I can't figure out how to make the table, though.
With the second table in b, I know how Q and not Q (~Q) relate, but cant see how to relate ~Q with (~PvR). If ~Q is false or (~PvR) is true, the implication is true. Again, I know how the implication works. It's this truth table that is making this problem vastly more difficult than it needs to be. Any help on filling them out is greatly appreciated.

2. Sep 8, 2011

micromass

Staff Emeritus
Do you have to fill them out in 4 rows?? That's weird.

The way I would handle it is to regard 8 possibilities:

P Q R
F F F
F F T
F T F
F T T
T F F
T F T
T T F
T T T

and fill in the rest.

3. Sep 8, 2011

Easy_as_Pi

Micro, you have came to rescue on a few of these problems for me. I really appreciate it. I don't think I have to fill it out in the way I did, but I was following the example in my book. None of them had three variables. Your method seems like the best. Thanks!