Checking containment in a Set of strings in Java

I have a Set of String[]. I want to check whether this Set contains another String[].

Set<String[]> s  = new HashSet<String[]>();
s.add(new String[] {"lucy", "simon"});
System.out.println(s.contains(new String[] {"lucy", "simon"}));

However, false is printed. My guess is this is because only the references are being compared and not the actual Strings. It seems, the only option I have is to create a class, say Phrase, and implement hashCode() and equals() (that use Arrays.hashCode(...)).

Is there any other way to achieve what I want?