Is the following statement a valid legal statement in Puppet code: package { 'resource-title' : name => $::operatingsystem ? { 'redhat' => $::memory ? { 512 => 'httpd', 128 => 'http', } 'debian' => 'apache2', }, ensure => installed, }?

The statement presented is not valid due to its syntax issues. In Puppet, conditional expressions using the ternary operator or similar constructs need to be properly formatted with appropriate syntax.

In this case, there are several issues with the way the nested conditional expressions are structured. Specifically, the second conditional check for $::memory is missing correct punctuation and structure, which makes it difficult for Puppet to interpret the conditions accurately. Additionally, each branch of a conditional must be properly separated from one another by commas and the outer structure must also correctly handle the result of the checks.

The 'package' resource requires a clear mapping of conditions to actions or outcomes, and the lack of proper syntax will cause Puppet to throw an error, indicating that the code is not valid. Therefore, the statement fails to compile, confirming that it is indeed an invalid legal statement in Puppet code.