"... I want to finally start making my code shorter."

You could use push() just once in the line:

any{$x == $_ } @y ? push(@z, "y") : push(@z, "n");
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by writing:

push @z, any {$x == $_ } @y ? "y" : "n";
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That's really just intended as an example. stevieb has provided an excellent response with a complete script above.

"I really want to use the ? : ; scheme properly ..."

Take a look at: Short form (ternary) if else. It discusses many aspects of ternary operator usage.