Problem 38

① The negation of "If $x^2+y^2 \neq 0$, then neither $x$ nor $y$ is zero" is:
"If $x^2+y^2 = 0$, then both $x$ and $y$ are zero", which is a true statement;
② The converse of "All isosceles triangles are similar" is:
"All similar triangles are isosceles triangles", which is a false statement;
③ For "If $m > 1$, then the solution set of the inequality $x^2+2x+m > 0$ is $\mathbb{R}$",
since $m > 1$, then $\Delta = 4-4m 1$, then the solution set of the inequality $x^2+2x+m > 0$ is $\mathbb{R}$" is a true statement,
therefore, the contrapositive of "If $m > 1$, then the solution set of the inequality $x^2+2x+m > 0$ is $\mathbb{R}$" is also a true statement.
Hence, the correct choice is $\boxed{B}$.