As mentioned by @Ryan you can use sets. In which case Set#subset? is available to you which is pretty readable (note the two different ways of defining a set from an array):
require 'set'
s1 = Set.new([1, 2, 3])
s2 = [1, 2].to_set
s3 = [1, 3].to_set
s4 = [1, 4].to_set
s1.subset? s1 #=> true
s2.subset? s1 #=> true
s3.subset? s1 #=> true
s4.subset? s1 #=> false
Also consider using Set#proper_subset if required.
s1.proper_subset? s1 #=> false
s2.proper_subset? s1 #=> true
NB A set contains no duplicate elements e.g. Set.new([1,2,3,3]) #=> #<Set: {1, 2, 3}>