3. Let S be a set. Recall that the power set P(S) with the symmetric difference operation is an abelian group; you may use this fact below. For elements A, BE P(S) let's write the symmetric difference operation as addition and the intersection operation as multiplication, so A+B means A AB, which is defined as (A - BU(B - A), and A. B means An B. 1. Show that P(S) with these addition and multiplication operations is a ring. (In this problem, to show an equation involving sets is true, instead of proving it you can just illustrate both sides of the equation with a Venn diagram.) II. Is this ring commutative? What is its zero element? Does it have a unity? Which elements are invertible? Is it a field? Explain your answers. a 3. Let S be a set. Recall that the power set P(S) with the symmetric difference operation is an abelian group; you may use this fact below. For elements A, BE P(S) let's write the symmetric difference operation as addition and the intersection operation as multiplication, so A+B means A AB, which is defined as (A - BU(B - A), and A. B means An B. 1. Show that P(S) with these addition and multiplication operations is a ring. (In this problem, to show an equation involving sets is true, instead of proving it you can just illustrate both sides of the equation with a Venn diagram.) II. Is this ring commutative? What is its zero element? Does it have a unity? Which elements are invertible? Is it a field? Explain your answers. a