For truth tables and the biconditional proposition operator, how comes false <--> false is true?
It seems counter intuitive, if I may make a stab at sounding mathematical.
Thanks!
For truth tables and the biconditional proposition operator, how comes false <--> false is true?
It seems counter intuitive, if I may make a stab at sounding mathematical.
Thanks!
Hello, Truthbetold!
For truth tables and the biconditional proposition operator,
how come $\displaystyle F \leftrightarrow F$ is true?
The biconditional $\displaystyle p \leftrightarrow q$ means that $\displaystyle \,p$ and $\displaystyle \,q$ have the same truth value.
Hence: .$\displaystyle \begin{Bmatrix} T\leftrightarrow T\, \text{ is true.} \\ F \leftrightarrow F\,\text{ is true.} \end{Bmatrix}$
I think the real problem here, and the one on which yours lays, might be: why the value of $\displaystyle A\rightarrow B$ is true
whenever the value of $\displaystyle A$ is false, no matter what the value of $\displaystyle B$ is?
The short answer is that it is so because it is defined so. Period. The long answer may pass through all kinds
of explantions including what truth really is and stuff. You may want to grab a book with some history of logic in it and read it.
Tonio