let P$_n$ be the following statement: Every group of n persons that contains at least on male contains only males. What is wrong with the following proof by induction that this statement is true for all n? Certainly P$_1$ is true. Now assume that P$_n$ is true, and take any group of n+! persons containing at least one male. Let G={p$_1$,p$_2$,p$_3$,...p$_n$,p$_n$$_+$$_1$} denote this group, with p$_1$ being known male. The subgroup {p$_1$,p$_2$,p$_3$,...p$_n$} of G must contain only males, by the induction assumption. Furthermore the n-person group {p$_2$,p$_3$,...p$_n$,p$_n$$_+$$_1$}, which we now know contains some males, must also contain only males, again using the induction assumption. Thus G consists of all males; p$_n$$_+$$_1$ follows
from
p$_n$.
I don't know where to start or anything. Any help or hints would be helpful.
You might be able to prove that $\{p_2,\cdots,p_{n+1}\}$ contains at least some male, but I cannot. Shows what I know, I guess.