--%>
Assignment Help - homework help

Elementary Logic Set & Model of a Boolean Algebra

Prove that Elementary Logic Set is a Model of a Boolean Algebra

The three Boolean operations of Logic are the three logical operations of  OR ( V ), AND (upside down V), and NEGATION ~.  Addition is the logical OR , multiplication is the logical AND, and complement is the logical NEGATION.  The symbol 1 is the logical T (True), and the symbol 0 is the logical F (False) . (Just state the Boolean Algebra versions of logical statements below, the proofs are considered self-evident, we do not require Truth Tables 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 F is an additive identity __________________________________

4. State the commutative law of multiplication: _____________________________________

5. State the associative law of multiplication: _______________________________________

6. State the law that says T 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 logical statement A.

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

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

11. In Elementary Logic, A implies B ( A-> B), has a Truth table, which we recall is only False (F), when B is False and A is True.  Rewrite the logical statement

A -> B in terms of the basic logical operations of AND (upside down V, we will have to use in this document the symbol ?), OR (V) and NEGATION (~).

A -> B =   

12. In terms of an Abstract Boolean Algebra, for two elements x and y define that x implies y,  x -> y using the basic operations  +,  •, and ~ of  Boolean Algebra, using the definition from Elementary Logic as your guide.

x -> y  

Recall that in Elementary Logic a Tautology is a statement which is always True, regardless of the truth values of its constituent statements., e.g.  A V ~A .

13. Write the Truth table for the logical statement (A->B)  V (B->A).   

Is (A->B)  V (B->A)  a tautology?

14. Write the Truth table for the logical statement  (B ? (A->B) ) ->A  (recall ? is unfortunately our symbol for AND, the upside down V).   

Is (B ? (A->B) ) ->A a tautology?

   Related Questions in Mathematics

  • Q : Problem on budgeted cash collections

    XYZ Company collects 20% of a month's sales in the month of sale, 70% in the month following sale, and 5% in the second month following sale. The remainder is not collectible. Budgeted sales for the subsequent four months are:     

    		•
  • Q : State Prime number theorem Prime number

    Prime number theorem: A big deal is known about the distribution of prime numbers and of the prime factors of a typical number. Most of the mathematics, although, is deep: while the results are often not too hard to state, the proofs are often diffic

    		•
  • Q : Problem on mixed-strategy equilibrium

    Assume three Offices (A, B, & C) in downtown,  simultaneously decide whether to situate in a new Building. The payoff matrix is illustrated below. What is (are) the pure stratgy Nash equilibrium (or equilibria) and mixed-strtegy equilibrium of the game?

    		•
  • Q : Linear programming model of a Cabinet

    A cabinet company produces cabinets used in mobile and motor homes. Cabinets produced for motor homes are smaller and made from less expensive materials than those for mobile homes. The home office in Dayton Ohio has just distributed to its individual manufacturing ce

    		•
  • 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 : Problem on Fermats method A public key

    A public key for RSA is published as n = 17947 and a = 3. (i) Use Fermat’s method to factor n. (ii) Check that this defines a valid system and find the private key X.

    Q : Who derived the Black–Scholes Equation

    Who derived the Black–Scholes Equation?

    		•
  • Q : Probability and Stochastic assignment

    Introduction to Probability and Stochastic Assignment 1: 1. Consider an experiment in which one of three boxes containing microchips is chosen at random and a microchip is randomly selected from the box.

    		•
  • Q : Elasticity of Demand For the demand

    For the demand function D(p)=410-0.2p(^2), find the maximum revenue.

    		•
  • Q : Law of iterated expectations for

     Prove the law of iterated expectations for continuous random variables. 2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution that satisfies the bounds exactly for k ≥1, show that it satisfies the bounds exactly, and draw its PDF. T

    		•