- #1

Easy_as_Pi

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## Homework Statement

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)

## 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 can't 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.