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.

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- Oct 7th 2011, 01:49 PMIDontunderstandIf 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 PMPlatoRe: If p then Q truth table
- Oct 7th 2011, 04:32 PMIDontunderstandRe: If p then Q truth table
I did mean rows.

- Oct 7th 2011, 06:02 PMSorobanRe: 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 didget an "A".*not*

. . .He broke his promise . . . call your lawyer!

(3) You didget 100% and you got an "A".*not*

. . .Maybe you got "only" 99% and your average is still "A".

. . .No basis for a lawsuit.

(4) You didget 100% and you did*not*get an "A".*not*

. . .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 you100% on the final.*got*

No promises were made about what would happen if you didget 100%.*not*

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