Solution Found!
For each set S, let peS) denote the set of all subsets of S. For A ,B E P(S), define A +
Chapter 24, Problem 24.22(choose chapter or problem)
For each set S, let peS) denote the set of all subsets of S. For A ,B E P(S), define A + B andABbyA + B 0: (A U B)\(A n B) = {x: x E AU B and x fj A n B)andAB=AnB.Verify that with these operations, F'(S) is a ring. [peS) is called the power set of A. SeeAppendix A for facts about sets. Suggestion: Make generous use of Venn diagrams in thisproblem.)
Questions & Answers
QUESTION:
For each set S, let peS) denote the set of all subsets of S. For A ,B E P(S), define A + B andABbyA + B 0: (A U B)\(A n B) = {x: x E AU B and x fj A n B)andAB=AnB.Verify that with these operations, F'(S) is a ring. [peS) is called the power set of A. SeeAppendix A for facts about sets. Suggestion: Make generous use of Venn diagrams in thisproblem.)
ANSWER:Step 1 of 8
Let be a non-empty set and be the set all subsets of .
Show that is a ring with the following operations
It is enough to show that is Abelian group and semi-group and also satisfies the distributive properties.