You could create a set of these values, and use Set.IsProperSubsetOf<'T>
to check for whether the values are contained.
let list1 = ['a';'b';'c']
let list2 = ['a';'x';'y';'b';'c';'e']
let list3 = ['a';'x';'a';'y';'c';'e']
let first = Set.ofList list1
let second = Set.ofList list2
let third = Set.ofList list3
let containedInSecond = first.IsProperSubsetOf second
let containedInThird = first.IsProperSubsetOf third
Running this in F# Interactive will print (for the last two lines) your desired results:
val containedInSecond : bool = true
val containedInThird : bool = false