Chapter 3: Q44E-a (page 59)
Let Sbe a set and let P(S) be the set of all subsets of S. Define addition and multiplication in P(S) by the rules
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(a) Prove that P(S) is a commutative ring with identity. [The verification of additive associativity and distributivity is a bit messy, but an informal discussion using Venn diagrams is adequate for appreciating this example. See Exercise 19 for a special case.]
Short Answer
It is proved that P(S) is a commutative ring with identity.