Cheat sheet of one 3 times 5 index card allowed. You can use scrap paper to aid
ID: 3583420 • Letter: C
Question
Cheat sheet of one 3 times 5 index card allowed. You can use scrap paper to aid you, but the final work is to be done on these sheets, and that is the work that is graded. No work equals No credit. Set Theory as a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union union Intersection intersection and complement ~. Addition is set union, multiplication it set intersection, and the complement of a set is the set all elements that are in the universal set, but not in the set. The universal set is the set of which all other sets are subsets and the empty set is the set, which has no elements and which therefore all other sets contain. For purposes of this question, let S denote the universal set and empty set the empty set. (Just state the Boolean algebra equalities of sets below, the proofs are considered self-evident. Let A, B, C denote arbitrary sets, instead of x, y, z, etc. and use the set theory operators listed above.) State the commutative law of addition: State the associative law of addition: State the law that says empty set is an additive identity State the commutative law of multiplication: State the associative law of multiplication: State the law that says S is a multiplicative identity State the distributive law of multiplication: State the distributive law of addition: State the Boolean algebra property x + (-^x) = 1 in terms of a set A. State the Boolean algebra property x middot (-^x) = 0 in terms of a set A. These statements prove Set Theory is a model of a Boolean algebra.Explanation / Answer
1. State the commutative law of addition: A B = B A
2. State the associative law of addition: A (B C) = (A B) C
3. State the law that says ' ' is an additive identity: A = A
4. State the commutative law of multiplication: A B = B A
5. State the associative law of multiplication: A (B C) = (A B) C
6. State the law that says S is a multiplicative identity A S = A
7. State the distributive law of multiplication: A (B C) = (A B) (A C)
8. State the distributive law of addition: A (B C) = (A B) (A C)
9. State the Boolean algebra property x + ~ x = 1 in terms of a set A: A ~A = U
10. State the Boolean algebra property x . ~ x = 0 in terms of a set A: A ~A =