I(S;X,Y)=H(S)+H(X,Y)−H(S,X,Y)=H(S)+H(X)+H(Y)−H(S,X,Y)
I(S;X)=H(S)+H(X)−H(S,X)
I(S;X,Y)−I(S;X)=H(Y)+H(S,X)−H(S,X,Y)=I(Y;S,X)≥I(S;Y)
For a visualization, see information diagrams, and note that the central cell I(S; X; Y) must be non-positive (because I(S; X; Y) + I(X; Y | S) = I(X; Y) = 0).
I(S;X,Y)=H(S)+H(X,Y)−H(S,X,Y)=H(S)+H(X)+H(Y)−H(S,X,Y)
I(S;X)=H(S)+H(X)−H(S,X)
I(S;X,Y)−I(S;X)=H(Y)+H(S,X)−H(S,X,Y)=I(Y;S,X)≥I(S;Y)
For a visualization, see information diagrams, and note that the central cell I(S; X; Y) must be non-positive (because I(S; X; Y) + I(X; Y | S) = I(X; Y) = 0).