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

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Discussion Overview

The discussion revolves around the truth tables for the logical implications P → Q and its converse Q → P, specifically in the context of the statements "I live in Paris" (P) and "I live in France" (Q). Participants are examining the validity and interpretation of these truth tables, as well as the implications of their truth values.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the truth table for Q → P, particularly regarding the second and third lines, and seeks clarification on why their desired truth values do not align with the table.
  • Another participant asserts that Q → P is incorrect in reality, questioning the expectation of correct results from it.
  • Some participants explain that if Q is false, then Q → P is always true, and that the only scenario in which Q → P can be false is when Q is true and P is false.
  • A later reply emphasizes that Q → P is not universally true in reality, suggesting a distinction between logical truth and real-world applicability.
  • One participant reiterates their confusion and states that the truth table for Q → P is identical to that for P → Q, noting that the rows are merely exchanged.

Areas of Agreement / Disagreement

Participants express differing views on the validity of Q → P in reality, with some asserting it is incorrect while others focus on the logical structure of the truth table. The discussion remains unresolved regarding the implications of these statements and their truth values.

Contextual Notes

There is an ongoing uncertainty regarding the interpretation of the truth values in the context of real-world scenarios versus logical implications. Participants have not reached a consensus on the correctness of the statements or the truth tables.

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

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

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.
 

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