If I have a proposition saying that if this function F(n) "x^(n)-1" = a composite number, then "n" is also composite is not always true.
I want to say that if F is a composite number then n is not. So basically if P then not Q. This is proven to be very difficult as most numbers that I can do in my head adds up. Can I switch the role around?
Can I go from "If P then Not Q" To "If Not P, then Q"?
And if so ,is it done by just doing this?: "Not (if P then Not Q)"?
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The implication $P\Rightarrow Q$ is logically equivalent to $\neg Q\Rightarrow \neg P$. So ''if $F$ is composite, then $n$ is not composite" is equivalent to "if $n$ is composite, then $F$ is not composite''.