If S \(\subset\) T \(\subset\) W, S \(\cap\) T \(\cap\) W = S is true since S \(\cap\) T = S and S \(\cap\) W = S. S \(\cup\) T \(\cup\) W = W is also true. S \(\cup\) T = T and T \(\cup\) W = W. However, to say that T \(\cap\) W = S is not very true mathematically. Instead, it is safe to say S \(\subset\) (T \(\cap\) W).