--%>
Assignment Help - homework help

Set Theory & Model of a Boolean Algebra

II. Prove that Set Theory is a Model of a Boolean Algebra

The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set union, multiplication is 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 Ø the empty set. (Just state the Boolean Algebra equalities of sets below, the proofs are considered self-evident, we do not require Venn diagrams to be written to establish their validity.)

1. State the commutative law of addition: _________________________________________

2. State the associative law of addition: _____________________________________________

3. State the law that says Ø is an additive identity __________________________________

4. State the commutative law of multiplication: ____________________________________

5. State the associative law of multiplication: _______________________________________

6. State the law that says S is a multiplicative identity _____________________________

7. State the distributive law of multiplication: ______________________________________

8. State the distributive law of addition: _____________________________________________

9.   State the Boolean Algebra property x  +  ˜ x  = 1 in terms of a set A.

10. State the Boolean Algebra property x  •  ˜ x  = 0 in terms of a set A.

The above ten properties are necessary and sufficient conditions to prove that Set Theory is indeed a model of a Boolean algebra.

11. In Set Theory the difference of two sets, A and B is defined as:

A - B = { s | s  belongs to A and s does not belong to B } 

Define the difference of two sets A and B, using the basic operations of set theory: union, intersection, and complement.

A - B =            

12. In terms of an Abstract Boolean Algebra, for two elements x and y define the difference, x - y using the basic operations  +,  •, and ~ of  Boolean Algebra, using the definition from Set Theory as your guide.

x - y  

13.  In Boolean Algebra rewrite the expression  x - (y + z) using only the basics operations of ~ , • and  +.

x - ( y + z ) = 

14.  Using the results of Boolean Algebra in problem 13 above, rewrite  the set theoretic expression of A - ( B U C ) using only the basics operations of set theory : union, intersection, and complement.

A - ( B U C ) = 

   Related Questions in Mathematics

  • Q : Formulating linear program of a

    A software company has a new product specifically designed for the lumber industry. The VP of marketing has been given a budget of $1,35,00to market the product over the quarter. She has decided that $35,000 of the budget will be spent promoting the product at the nat

    		•
  • Q : Set Theory & Model of a Boolean Algebra

    II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set

    		•
  • Q : Pig Game Using the PairOfDice class

    Using the PairOfDice class design and implement a class to play a game called Pig. In this game the user competes against the computer. On each turn the player rolls a pair of dice and adds up his or her points. Whoever reaches 100 points first, wins. If a player rolls a 1, he or she loses all point

    		•
  • Q : Properties of a group How can we say

    How can we say that the pair (G, o) is a group. Explain the properties which proof it.

    		•
  • Q : How do it? integral e^(-t)*e^(tz) t

    integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1

    		•
  • Q : Formal logic It's a problem set, they

    It's a problem set, they are attached. it's related to Sider's book which is "Logic to philosophy" I attached the book too. I need it on feb22 but feb23 still work

    		•
  • Q : Global And Regional Economic Development

    The Pharmatec Group, a supplier of pharmaceutical equipment, systems and services, has its head office in London and primary production facilities in the US. The company also has a successful subsidiary in South Africa, which was established in 1990. Pharmatec South A

    		•
  • Q : What is Big-O hierarchy The big-O

    The big-O hierarchy: A few basic facts about the big-O behaviour of some familiar functions are very important. Let p(n) be a polynomial in n (of any degree). Then logbn is O(p(n)) and p(n) is O(an<

    		•
  • Q : Numerical solution of PDE this

    this assignment contains two parts theoretical and coding the code has to be a new. old code and modified code will appear in the university website .

    		•
  • Q : Explain Factorisation by Fermats method

    Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the di fference of two squares.

    		•