Let A = {t, u, v, w}, and let S1 be the set of all subsets of A that do not contain w, and S2 the set of all subsets of A that contain w. (a) Find S1. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.)

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

Step-by-step explanation:

Given:

A = {t, u, v, w}

S1 = set of all subsets of A that do not contain w.

S2 = set of all subsets of A that contains w.

Therefore S1 & S2 in set roster notation will be given as:

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

S2 = { {w}, {t,w}, {u,w}, {v,w}, {t,u,w}, {t,v,w}, {u,v,w}, {t,u,v,w} }

a) We can see that,

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

the answer is 62.8 cubic units

part a: 1.08

part b: 27.59