Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
II. Prove that Set Theory is a Model of a Boolean Algebra <br/> <br/>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.) <br/> <br/>1. State the commutative law of addition: _________________________________________ <br/> <br/>2. State the associative law of addition: _____________________________________________ <br/> <br/>3. State the law that says Ø is an additive identity __________________________________ <br/> <br/>4. State the commutative law of multiplication: ____________________________________ <br/> <br/>5. State the associative law of multiplication: _______________________________________ <br/> <br/>6. State the law that says S is a multiplicative identity _____________________________ <br/> <br/>7. State the distributive law of multiplication: ______________________________________ <br/> <br/>8. State the distributive law of addition: _____________________________________________ <br/> <br/>9. State the Boolean Algebra property x + ˜ x = 1 in terms of a set A. <br/> <br/>10. State the Boolean Algebra property x • ˜ x = 0 in terms of a set A. <br/> <br/>The above ten properties are necessary and sufficient conditions to prove that Set Theory is indeed a model of a Boolean algebra. <br/> <br/>11. In Set Theory the difference of two sets, A and B is defined as: <br/> <br/>A - B = { s | s belongs to A and s does not belong to B } <br/> <br/>Define the difference of two sets A and B, using the basic operations of set theory: union, intersection, and complement. <br/> <br/>A - B = <br/> <br/>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. <br/> <br/>x - y <br/> <br/>13. In Boolean Algebra rewrite the expression x - (y + z) using only the basics operations of ~ , • and +. <br/> <br/>x - ( y + z ) = <br/> <br/>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. <br/> <br/>A - ( B U C ) =
The price of a technology stock has risen to today. Yesterday's price was . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Derive the Boolean Expression and construct the switching circuit for the truth table stated
The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area.
What is the difference between prime numbers and composite numbers? How are prime numbers and composite numbers related? Prime numbers are often used in cryptography.
Find the solution to the given system for the given initial condition
How many different passwords can be formed? b) How many different passwords have no repeated number or letters?
A box with its base in the xy-plane has its four upper vertices on the surface with equation z=48-3x^2-4y^2. What is the maximum possible volume.
A 150kg horizontal beam is supported at each end. A 380-kg piano rests a quarter of the way from one end. What is the vertical force on each of the supports?
What is the correct conclusion for this hypothesis test?
how does each key managerial dimension promote effective research? how does each dimension help meet desired results?
In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).
He then traveled 24 km at a speed that was 4 km h slower. If the total time for Tims trip was 8 hr, what was his speed on each part of the trip?
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd