In his book, Axioms & Set Theory, Robert Andre introduces logic with this statement:

If $Q$ is true whenever $P$ is true, and $T$ is true whenever $Q$ is true, then $T$ is true whenever $P$ is true.

He renders the statement symbolically:

$$[(P \Rightarrow Q) \land (Q \Rightarrow T)] \Rightarrow T$$

How is this so? The symbols seem to say:

If $Q$ is true whenever $P$ is true, and $T$ is true whenever $Q$ is true, then $T$ is true.

It seems to me that the English statement given by Andre would be rendered

$$[(P \Rightarrow Q) \land (Q \Rightarrow T)] \Rightarrow [P \Rightarrow T]$$

What am I missing?

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    $\begingroup$ Looks like the book has a typo. You're right. $\endgroup$ – Mark S. Jun 12 '17 at 0:00
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    $\begingroup$ You missed nothing, it is a (big) typo. Now go back to sleep , if it's 4:00am over there ;-) $\endgroup$ – magma Jun 12 '17 at 7:18
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    $\begingroup$ “Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering."/Yoda $\endgroup$ – skyking Jun 12 '17 at 10:57
  • $\begingroup$ Robert Andre is a sith... he wanted to say that all implications leads to the dark side... $\endgroup$ – Brethlosze Jun 12 '17 at 14:51

Your statement is correct since it reduces to $[P \implies T] \implies [P \implies T]$ which is a tautology(Always true),

Andre's statement however reduces to $[P \implies T] \implies T ]$ which is a false statement if both P and T are false.

As a side note this makes you right since proving logical correctness of a statement is the same as reducing it to a tautology


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