--%>
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 : State Fermat algorithm The basic Fermat

    The basic Fermat algorithm is as follows: Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers c2 - n; (c+1)2 - n; (c+2)2 - n..... until a perfect square is found. If th

    		•
  • Q : Solve each equation by factoring A

    A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%.  If his annual interest is $1,670 how much did he invest at 6%?  If I told you the answer is $8,000, in your own words, using complete sentences, explain how you

    		•
  • Q : Row-echelon matrix Determine into which

    Determine into which of the following 3 kinds (A), (B) and (C) the matrices (a) to (e) beneath can be categorized:       Type (A): The matrix is in both reduced row-echelon form and row-echelon form. Type (B): The matrix

    		•
  • 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 : 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 : 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 : 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.

    		•
  • Q : The mean of the sampling distribution

    1. Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If P-hat is the proportion saying that the food is delicious, what is the mean of the sampling distribution p-hat?<

    		•
  • Q : Who developed a rigorous theory for

    Who developed a rigorous theory for Brownian motion?

    		•
  • Q : Research Areas in Medical Mathematical

    Some Research Areas in Medical Mathematical Modelling:1. Modeling and numerical simulations of the nanometric aerosols in the lower portion of the bronchial tree. 2. Multiscale mathematical modeling of

    		•