--%>
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 : How do it? integral e^(-t)*e^(tz) t

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

    		•
  • Q : Probability assignments 1. Smith keeps

    1. Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20substandard? 2. Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2

    		•
  • 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 : Examples of groups Examples of groups:

    Examples of groups: We now start to survey a wide range of examples of groups (labelled by (A), (B), (C), . . . ). Most of these come from number theory. In all cases, the group axioms should be checked. This is easy for almost all of the examples, an

    		•
  • 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 : Problem on reduced row-echelon The

    The augmented matrix from a system of linear equations has the following reduced row-echelon form. 280_row echelon method.jpg

    		•
  • Q : Test Please read the assignment

    Please read the assignment carefully and confirm only if you are 100% sure. Please go through below mentioned guidelines and penalties: • Your solution must be accurate and complete. • Please do not change Subject Title of the Email. • Penalty clause will be applied in case of delayed or plag

    		•
  • Q : Who firstly discovered mathematical

    Who firstly discovered mathematical theory for random walks, that rediscovered later by Einstein?

    		•
  • Q : What is Non-Logical Vocabulary

    Non-Logical Vocabulary: 1. Predicates, called also relation symbols, each with its associated arity. For our needs, we may assume that the number of predicates is finite. But this is not essential. We can have an infinite list of predicates, P

    		•
  • 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

    		•