# Need help with truth table for P->Q and it's inverse

1. Mar 3, 2013

### Mofasa

Hi!

I'm struggling with the bellow truth tables:

P = I live in Paris
Q = I live in France

A B C
P → Q Q → P ¬ Q → ¬ P
S S S S S S F S F
S F F F S S S F F
F S S S F F F S S
F S F F S F S S S

Table A and C I'm fully clear with. However I don't understand the truth table for B (the converse of P → Q).

Table B:

Q → P
S S S
F S S
S F F
F S F

If I live in France there is a possibility I live in Paris S (Understand)
If I don't live in France there is a possibility I live in Paris S (Don't understand)
If I live in France there is not a possibility I live in Paris F (Don't understand)
I I don't live in France there is not a possibility I live in Paris S (Understand)

I want line 2 to be false and line 3 to be true.

Can someone explain why this should not be the case?

Last edited: Mar 3, 2013
2. Mar 3, 2013

### Staff: Mentor

Q → P ("If I live in France, I live in Paris") is wrong in reality, why do you expect correct results for this?

3. Mar 3, 2013

### micromass

Staff Emeritus
If Q is false, then $Q\rightarrow P$ is always a true statement. So if you don't live in France, then the statement "If I live in France, then I live in Paris" is true.

The only way $Q\rightarrow P$ can ever be false is if $Q$ is true and $P$ is false.

4. Mar 3, 2013

### Staff: Mentor

Okay, to be more precise: Q → P is not true in general (=for all) in reality.

5. Mar 4, 2013

### Bacle2

The truth table for Q→P is exactly the same as that for P→Q , since they are both

plain/standard conditionals. Notice that the tables are exactly the same except

rows 2 and 3 have been exchanged.