# If p then Q truth table

• Oct 7th 2011, 01:49 PM
IDontunderstand
If p then Q truth table
p q p-->q
T T T
T F F
F T T
F F T

Why do the last two columns in the truth table equal True? This really does not make any sense to me.
• Oct 7th 2011, 01:54 PM
Plato
Re: If p then Q truth table
Quote:

Originally Posted by IDontunderstand
p q p-->q
T T T
T F F
F T T
F F T

Why do the last two columns in the truth table equal True? This really does not make any sense to me.

I think that you mean rows.
A false statement implies any statement.
If false then anything is true.
• Oct 7th 2011, 04:32 PM
IDontunderstand
Re: If p then Q truth table
I did mean rows.
• Oct 7th 2011, 06:02 PM
Soroban
Re: If p then Q truth table
Hello, IDontunderstand!

Plato is absolutely correct . . .

I too was puzzled when I first learned about Implication.
This is how my professor explained it.

Consider this scenario.

Your professor makes you this promise:
. . If you get 100% on the final exam, then you will get an "A" for the course.
(Imagine further than you don't trust him, so you get this in writing,
. . signed and notarized before witnesses!)

Under what circumstances has he broken his promise,
. . (and you can start a class-action suit)?

Consider the four possible outcomes:

(1) You got 100% on the Final and you got an "A" for the course.
. . .He kept his promise . . . no problem!

(2) You got 100% on the Final and you did not get an "A".
. . .He broke his promise . . . call your lawyer!

(3) You did not get 100% and you got an "A".
. . .Maybe you got "only" 99% and your average is still "A".
. . .No basis for a lawsuit.

(4) You did not get 100% and you did not get an "A".
. . .Maybe you got only 60% and your average dropped to a "B".
. . .Again, no basis for a lawsuit.

In brief: his promise involves only what would happen if you got 100% on the final.
No promises were made about what would happen if you did not get 100%.

And that is why .$\displaystyle \begin{Bmatrix} T \to T \\ F \to T \\ F \to F\end{Bmatrix}$ are all True.