Use the following definitions. Let X = {a, b, c}. Define a function S from  to the set of...

Use the following definitions. Let X = {a, b, c}. Define a function S from  to the set of bit strings of length 3 as follows. Let Y ⊆ X. If a ϵY, set s1 = 1; if a ∉ Y, set s1= 0. If b ϵ Y. set s2 = 1; if b ∉Y, set s2 = 0. If c ϵ Y, set s3 = 1; if c ∉Y, set s3 = 0. Define S(Y) = s1.s2.s3

 What is the value of S(∅ )?