--%>
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 : Mathematical and Theoretical Biology

    Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in the fields of biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical

    		•
  • 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 : Explain Black–Scholes model Explain

    Explain Black–Scholes model.

    		•
  • 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 : Define Well-formed formulas or Wffs

    Wffs (Well-formed formulas): These are defined inductively by the following clauses:    (i) If  P  is an n-ary predicate and  t1, …, tn are terms, then P(t1, …, t

    		•
  • 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 : Profit-loss based problems A leather

    A leather wholesaler supplies leather to shoe companies. The manufacturing quantity requirements of leather differ depending upon the amount of leather ordered by the shoe companies to him. Due to the volatility in orders, he is unable to precisely predict what will b

    		•
  • 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 inventory merchandise AB

    AB Department Store expects to generate the following sales figures for the next three months:                            

    		•
  • Q : Elementary Logic Set & Model of a

    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 ), AN

    		•